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Topic: Quantum groups

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	Quantum Mechanics :: Physics
		Quantum mechanics is a fundamental branch of theoretical physics that replaces classical mechanics and classical electromagnetism at the atomic and subatomic levels.
		Along with general relativity, quantum mechanics is one of the pillars of modern physics.
		An introduction to Quantized Lie Groups and Algebras: We give a selfcontained introduction to the theory of quantum groups according to Drinfeld highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory.
	science.gourt.com /Physics/Quantum-Mechanics.html (1036 words)

	Operator algebras and quantum groups (Site not responding. Last check: 2007-10-30)
		They are important not only for quantum physics - their theory has a vast range of applications in such areas as differential geometry, algebraic topology, group theory, knot theory, classical dynamical systems and many other areas.
		Quantum groups were introduced as generalisations of these symmetry groups.
		However, they are not groups (despite the name); rather, in their modern formulation, they are C*-algebras with an associated Hopf algebra structure.
	www.irishscientist.ie /2000/contents.asp?contentxml=190bs.xml&contentxsl=insight3.xsl (471 words)

	Quantum groups with invariant integrals -- Van Daele 97 (2): 541 -- Proceedings of the National Academy of Sciences
		There are several approaches to quantum groups, but all of them have a common idea.
		This paper is the first of two papers on the operator algebra approach to quantum groups; the second one is ref. 4.
		Quantum groups have been studied quite intensively for the last 15 years; this is mainly done in the algebraic context.
	www.pnas.org /cgi/content/full/97/2/541 (4058 words)

	NationalDirectory : Science Physics Quantum Mechanics (Site not responding. Last check: 2007-10-30)
		An introduction to Quantized Lie Groups and Algebras - We give a selfcontained introduction to the theory of quantum groups according to Drinfeld highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory.
		Quantum and Braided Spin - The modern Kaluza-Klein theories of unification of gauge fields and gravitation, the theories of grand unification and, more recently, superfield, super-string, membrane and conformal field theories have enhanced the role of the geometry of multidimensional spaces in fundamental theoretical physics.
		Topics in Modern Quantum Optics - This is the written version of lectures presented at the 17th Symposium on Theoretical Physics covering various topics in quantum optics.
	www.nationaldirectory.com /Science/Physics/Quantum_Mechanics (888 words)

	Research in Algebra \| Ring Theory
		It turns out that the representation theory of groups such as the general linear group and symmetric group is closely connected with Lie theory, through topics like the representation theory of algebraic groups and Lie algebras.
		They are related to quantum groups through work of Lusztig on canonical bases and Nakajima on quiver varieties, to singularity theory through work of Kronheimer (and then to Lie algebras), and the representation theory of any finite dimensional algebra can be understood through representations of quivers.
		James and M. Liebeck, Representations and Characters of Groups, C.U.P. Jantzen, Lectures on quantum groups, A.M.S. Jantzen, Representations of Lie algebras in prime characteristic, in Representation theories and algebraic geometry, Kluwer (1997).
	www.maths.gla.ac.uk /research/groups/algebra/rings.htm (987 words)

	Re: Hopf algebras, quantum groups
		Historically, it seems that quantum groups were invented independently by two groups: the Poles, led by Woronowicz, and the Russians, led by Faddeev.
		It took them a while to sort it out, but eventually it became clear: this quantum group came from quantizing the group of symmetries of the original classical field theory.
		I hope you see that quantum groups have a LOT of relationship to quantum mechanics, and there is really no way to deeply understand them without knowing quantum mechanics.
	www.lns.cornell.edu /spr/2001-01/msg0030352.html (1098 words)

	homep
		A hidden classical group structure is clearly indicated for all generic models of quantum groups.
		topology on quantum groups leads to a remarkable unification and rigidification of the different definitions, we adapt here, in the same way, the definition of quantum double.
		We show that the theory of quantum groups is a part of the theory of star-products and make a review of the results obtained with this approach.
	www.u-bourgogne.fr /monge/p.bonneau/preprint.html (740 words)

	On a class of representations of quantum groups (Site not responding. Last check: 2007-10-30)
		This paper is a short account of the construction of a new class of the infinite-dimensional representations of the quantum groups.
		At the intermediate step we construct the embedding of the quantum groups into the algebra of the rational functions on the quantum multi-dimensional torus.
		The explicit parameterization of the quantum groups used in this paper turns out to be closely related to the parameterization of the moduli spaces of the monopoles.
	www.maths.tcd.ie /report_series/abstracts/tcdm0501.html (139 words)

	LMS Regional Meeting - Abstracts (Site not responding. Last check: 2007-10-30)
		Recently the study of the symmetries of certain integrable quantum field theories with a boundary (principal chiral models and affine Toda theories) have led to the discovery of boundary quantum groups.
		Quantum affine algebra and Yangians were introduced by Drinfel'd as the algebraic structures behind trigonometric and rational solutions of the Yang-Baxter equation.
		The boundary quantum groups lead to the corresponding solutions of the reflection equation.
	www.cf.ac.uk /maths/opalg/lmsmeeting-abstracts.html (629 words)

	Quantum Groups at QMUL
		Just as Lie groups and their homogeneous spaces are basic examples of differentiable manifolds, so quantum groups and their associated algebras should be basic examples of a theory of noncommutative geometry, which has led to a kind of `quantum groups approach' to noncommutative geometry.
		In general, while one of the original motivations of the subject may have been quantum theory, there turn out to be many other motivations from deep within pure mathematics itself, such as discrete geometry, knot theory, representation theory and resolution of singularities.
		If you have some exposure to quantum theory then you may know that the whole point of the correspondence principle in quantum mechanics is that certain macroscopic concepts like position and momentum coordinates have analogues as noncommuting operators.
	www.maths.qmw.ac.uk /%7Emajid/qg.html (1192 words)

	Operator Algebras in University College Cork
		Quantum groups (Gerard Murphy) A unital C-algebra with a comultiplication is the quantum* analogue of a compact semigroup.
		Thus, the theory of quantum differential calculi is in some sense a "Type III" theory and it may be that it does not fit into Connes framework without further modification of that theory.
		Quantum probability (Steve Wills) My research is in quantum or noncommutative probability, a subject that combines mathematical physics, probability theory and functional analysis.
	euclid.ucc.ie /pages/staff/murphyg (737 words)

	Quantum groups with invariant integrals -- Van Daele 97 (2): 541 -- Proceedings of the National Academy of Sciences
		Quantum groups with invariant integrals -- Van Daele 97 (2): 541 -- Proceedings of the National Academy of Sciences
		Quantum groups have been studied intensively for the last two decades from various points of view.
		for the operator algebra approach to quantum groups.
	www.pnas.org /cgi/content/abstract/97/2/541 (192 words)

	gerard murphy
		My principal interests are in the general theory of C-algebras, the spectral and index theory of Toeplitz operators on Hardy spaces of ordered groups* and bounded symmetric domains, and the C-algebra approach to quantum* groups.
		It is directed at first and second year graduate students intending to specialise in research in operator algebras and at interested researchers from other areas, especially quantum physicists.
		Quantum groups, differential calculi and the eigenvalues of the Laplacian,
	euclid.ucc.ie /pages/staff/murphyg/gerardmurphy.htm (577 words)

	Anthony Joseph -Quantum Groups and Their Primitive Ideals Ergebnisse Der Mathematik Und Ihrer Grenzgebiete 3 Folge Band ... (Site not responding. Last check: 2007-10-30)
		Quantum Groups and Their Primitive Ideals Ergebnisse Der Mathematik Und Ihrer Grenzgebiete 3 Folge Band 29
		Quantum Geometry A Framework for Quantum General Relativity Fundamental Theories of Physics Vol 48.
		Quantum Group and Quantum Integrable Systems Nankai Lectures on Mathematical Physics Nankai Institute of Mathematics China 2 - 18 April 1991.
	www.reviewofbooks.net /297183quantum_groups_primitive_ideals_ergebnisse_mathematik_grenzgebiete_3_folge_band_29.html (112 words)

	Mathematical Physics - Department of Mathematics - University of York
		York has a large and friendly mathematical physics group with a wide range of research interests and an international outlook (rated 5 in the 2001 RAE).
		If you are interested in graduate study or post-doctoral research, please feel free to contact the relevant member of staff.
		The main areas of research are Quantum Gravity, Quantum Field Theory and Integrable Models, Quantum Information and Foundations of Quantum Mechanics, and Quantum Groups.
	www.york.ac.uk /depts/maths/physics/qg.html (163 words)

	Re: Hopf algebras, quantum groups
		If not, we should probably stick to U_h(sl(2)), which is everyone's favorite example, and the one most important in quantum gravity.
		I know various good books on quantum groups.
		I guess I'd recommend Christian Kassel's _Quantum Groups_ for a sober yet readable treatment, and Shahn Majid's _Foundations of Quantum Group Theory_ for a more idiosyncratic text which captures more of the wild-eyed excitement of the quantum group craze.
	www.lns.cornell.edu /spr/2001-01/msg0030375.html (375 words)

	Ian M. Musson, Publications
		On the Structure of Certain Injective Modules over Group Algebras of Soluble Groups of Finite Rank, J. of Algebra, 85 (1983) 51-75.
		Hopf algebras and quantum groups (Brussels, 1998), 177--188, Lecture Notes in Pure and Appl.
		Quantum groups and Lie theory (Durham, 1999), 191--205, London Math.
	www.uwm.edu /~musson/publica.html (562 words)

	Naturvidenskab, AU: Quantum groups
		Quantum groups were introduced independently some 15 years ago
		group is not a group but an algebra.
		aspects of its representation theory are very similar to that of the corresponding Lie algebra or Lie group.
	www.nat.au.dk /default.asp?la=dk&id=4031&aar=2001 (182 words)

	Quantum Groups at QM
		If you specifically want to work in our group then you should either have an interest in pure mathematics or in mathematical physics with a willingness to think creatively about abstract structures where relevant.
		Our interests in the group encompass a broad view of noncommutative geometry, quantum groups, representation theory and related topics in mathematical physics, including aspects of string theory and quantum gravity.
		The basic procedure for UK citizens to be considered on a competetive basis accross all maths subjects is to send an application form (which can be downloaded from the QM Website) to the graduate admissions tutor in the maths department as soon as possible and preferably before May for admission in September.
	www.maths.qmw.ac.uk /~majid/op.html (992 words)

	Books of Representation Theory
		Toshiyuki Tanisaki, Lie algebras and quantum groups, Kyoritsu-Shuppan (in Japanese), 2002.
		Gabor Toth, Finite Moebius groups, minimal immersions of spheres, and moduli, Universitext, Springer, 2002.
		Susumu Ariki, Representations and combinatorics on affine quantum group $ A_{r - 1}^{(1)} $, Lecture Notes of Sophia Univ., 2000.
	rtweb.math.kyoto-u.ac.jp /bookse.html (802 words)

	Florin Panaite
		Ph.D. in Mathematics, University of Bucharest, 1999, with the thesis "Algebras and coalgebras with applications to quantum groups", advisor Prof.
		My field of research is the theory of Hopf algebras and quantum groups, including extensions of these concepts (quasi-Hopf algebras, quantum groupoids etc).
		Quantum traces and quantum dimensions for quasi-Hopf algebras, Comm.
	www.imar.ro /~fpanaite (822 words)

	Amazon.com: A Guide to Quantum Groups: Books: Vyjayanthi Chari,Andrew N. Pressley (Site not responding. Last check: 2007-10-30)
		Since they first arose in the 1970s and early 1980s, quantum groups have proved to be of great interest to mathematicians and theoretical physicists.
		This book gives a comprehensive view of quantum groups and their applications.
		As we mentioned in the Introduction, one reason for the terminology used to describe 'quantum groups' is that their relation to ordinary Lie groups is analogous to that between quantum mechanics and classical mechanics.
	www.bizave.com /cgi-bin/redirectnolist.cgi/itemid=005215580084/extitem=1/title=STOREITEM:BOOK:A_Guide_to_Quantum_Groups (766 words)

	school
		The objective of this school is to provide an introduction to the theory of quantum stochastic processes with independent increments, ranging from their mathematical structure to their applications, e.g., as models for noise in quantum physics.
		The second week will deal with current research topics related to quantum independent increment processes and be of interest also to graduate students and young scientists working in operator algebras, (quantum) stochastics and quantum physics.
		An overview of examples of non-compact quantum groups together with a detailed discussion of the main peculiarities of their construction.
	www.math-inf.uni-greifswald.de /algebra/special/school.htm (570 words)

	[No title]
		(with J. Jantzen and W. Soergel) Representations of quantum groups at a p-th root of unity and of semisimple groups in characteristic p: Independence of p,
		The irreducible characters for semi-simple algebraic groups and for quantum groups,
		The strong linkage principle for quantum groups at roots of $1$,
	home.imf.au.dk /mathha/publ.html (481 words)

	Quantum Groups, Quantum Categories and Quantum Field Theory (Lecture Notes in Mathematics) by Jurg Frohlich, New, Used ...
		This book reviews recent results on low-dimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories.
		Representations of Lie Groups and Quantum Groups (...
		Algebraic Combinatorics and Quantum Groups (By Naihuan Jing)
	www.bookfinder4u.com /detail/0387566236.html (370 words)

	Math 274 - Fall 2004 (Site not responding. Last check: 2007-10-30)
		Structure of (quantum) affine algebras and their representations.
		V. Drinfeld, Quantum groups, Proceedings of the ICM, Berkeley, 1986.
		G. Lusztig, Introduction to Quantum Groups (Birkhauser, 1993).
	math.berkeley.edu /~mhaiman/math274/index.html (189 words)

	MI - Prof. Dr. Konrad Schmuedgen - Publikationen
		(with I. Heckenberger) Classification of bicovariant differential calculi on the quantum groups SLq(n+1) and Spq(2n).
		Commutator representations of differential calculi on the quantum group SUq(2).
		Commutator representations of covariant differential calculi on quantum groups.
	www.mathematik.uni-leipzig.de /MI/schmuedgen/publikationen.html (196 words)

	week48
		In particular, this means that the quantity folks like to compute whenever they see a quantum field theory --- the partition function, which you get by doing a path integral a la Feynman --- is an invariant of 3-dimensional manifold you happen to have taken as "spacetime".
		For example, the resulting "finite quantum group" does not depend on hbar; it's just the "quantum double" of the group algebra of the group.
		So one should be able to get ahold of quantum groups this way too: starting with the "moduli space of flat bundles" and "quantizing" it.
	math.ucr.edu /home/baez/week48.html (1285 words)

	Dr. István Heckenberger
		For bicovariant differential calculi on quantum matrix groups a generalisation of classical notions such as metric tensor, Hodge operator, codifferential and Laplace-Beltrami operator for arbitrary k-forms is given.
		Any bicovariant calculus is inner and its quantum Lie algebra is generated by a central element.
		For bicovariant differential calculi on quantum groups various notions on connections and metrics (bicovariant connections, invariant metrics, the compatibility of a connection with a metric, Levi-Civita connections) are introduced and studied.
	www.mathematik.uni-leipzig.de /MI/heckenberger/publ.html (823 words)

	Eight lectures on quantum groups and q - special functions (Site not responding. Last check: 2007-10-30)
		The lectures contain an introduction to quantum groups, q - special functions and their interplay.
		After generalities on Hopf algebras, orthogonal polynomials and basic hypergeometric series we work out the relation between the quantum SU(2) group and the Askey - Wilson polynomials in detail as the main example.
		Quantum groups, special functions, Hopf algebras, Askey - Wilson polynomials, addition formula, convolution.
	www.univie.ac.at /EMIS/journals/RCM/96300202.html (199 words)

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