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Topic: Nonabelian

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	[No title]
		Thus there is considerable evidence that the nonabelian fundamental group i* s naturally generalised to various forms of crossed modules or double groupoids, and that t *hese structures enable new understanding and calculations in dimension 2.
		Nonabelian Algebraic Topology * * 4 _________________________________
		This Nonabelian Algebraic Topology * * 6 can be seen as a rectification result, by which we mean a result using deformat* *ions to replace equations up to homotopy by strict equations.
	hopf.math.purdue.edu /BrownR/IMA-talk.txt (3300 words)

	FUB-HEP/95 Nonabelian Bosonization as a Nonholonomic Transformations from Flat to Curved Field Space.
		Nonabelian Bosonization as a Nonholonomic Transformations from Flat to Curved Field Space.
		There exists a simple rule by which path integrals for the motion of a point particle in a flat space can be transformed correctly into those in curved space.
		Here we point out its relevance in the process of bosonizing a nonabelian one-dimensional quantum field theory, whose fields live in a flat field space.
	www.physik.fu-berlin.de /~kleinert/kleiner_re239/paperpep.html (279 words)

	Talk at IIASS: Nonabelian Strings \| The String Coffee Table
		2-bundles, 2-connections and 2-holonomy and the relation to nonabelian gerbes.
		Intersections of membranes with stacks of M5-branes are expected to give rise to a dimensional generalization of nonabelian gauge theory from point particles to strings.
		A gerbe is a generalization of the concept of a sheaf of sections of a fiber bundle obtained by a method known as categorification.
	golem.ph.utexas.edu /string/archives/000532.html (586 words)

	Re: classical nonabelian particle
		That would >mean nonabelian gauge theory is somehow inherently quantum.
		Guillemin and Sternberg give a treatment of a classical charged particle in a nonabelian gauge field in their book "Symplectic Techniques in Physics".
		The key trick is to realize that the internal degrees of freedom of a "classical nonabelian charged particle" must be described using a space called a "coadjoint orbit".
	www.lns.cornell.edu /spr/2003-10/msg0055331.html (242 words)

	Group (mathematics) - Wikipedia, the free encyclopedia
		In fact, the nonzero elements of any given field form a group under multiplication, called the multiplicative group of the field.
		A finite nonabelian group: permutations of a set
		For a more concrete example, consider three colored blocks (red, green, and blue), initially placed in the order RGB.
	en.wikipedia.org /wiki/Mathematical_group (1904 words)

	Nonabelian Self-Duality \| The String Coffee Table
		When I talked to nonabelian gerbe people about this, one thing they said is that it is not clear that in the nonabelian case the self-duality should still be ordinary Hodge self-duality, but that it might involve in addition to the Hodge star an operation on the Lie algebra factor.
		The existence of that nonabelian 2-holonomy seems to be, apart from the self-duality of
		Therefore, in order to understand nonabelian theories in 6D (and, incidentally, the general configuration of the fundamental objects of M-theory) it would be very helpful to have a notion of nonabelian surface holonomy
	golem.ph.utexas.edu /string/archives/000485.html (1043 words)

	Open Questions: The Langlands Program
		Group representations provide a mechanism for generalizing harmonic analysis to deal with nonabelian groups.
		This generalized theory is fundamental to the Langlands program, and is applicable in many other areas as well, such as the theory of Lie groups.
		Nonabelian reciprocity laws can be expressed as an identity between L-functions defined in different ways.
	www.openquestions.com /oq-ma016.htm (372 words)

	Wolfgang Poeschl: What I do in my free time . . . (Site not responding. Last check: 2007-10-22)
		The rapid oscillations occurring during the overlap of the wave packets are caused by interference effects.
		The transversely polarized nonabelian wave packets are rapidly disintegrating after the collision.
		The destruction is caused by the exponential growth of perturbations due to the nonlinear interaction among the wave packets during their overlap.
	www.phy.duke.edu /~muller/BRAHMA/MOVIES/Movies.html (203 words)

	[No title]
		I don't know if this is the case when G is nonabelian discrete.
		In the abelian case G can be seen as a module over integers Z. Every cyclic Z-module embeds into a circle which is compact and injective as a Z-module hence the Bohr compactification can not have a kernel in this case.
		This proof did not assume that the homomorphism should be continuous; hence it works for G with the discrete topology.
	www.math.niu.edu /~rusin/known-math/99/compactification_grp (1216 words)

	Publication : T93/012
		We show how generic nonabelian gauge fields can be induced in baryons when a hierarchy of fast degrees of freedom is integrated out.
		We identify them with nonabelian Berry potentials and discuss their role in transmuting quantum numbers in bag and soliton models of baryons.
		the electronic rotational invariance in diatomic molecules, the heavy-quark symmetry in heavy baryons etc. is interpreted in terms of the vanishing of nonabelian Berry potentials that otherwise govern the hyperfine splitting.
	www-spht.cea.fr /articles/t93/012 (161 words)

	Physics Help and Math Help - Physics Forums - View Single Post - Towards nonabelian membrane action
		this nonabelian 2-form is described by nonabelian gerbes.
		nonabelian gerbes I don't mean that there is a proof that none exists.
		the connection and curving of a nonabelian gerbe.
	www.physicsforums.com /showpost.php?p=417662&postcount=5 (1110 words)

	Hilbert Space of Bosonized Nonabelian Model
		In the abelian case, the Green functions of the initial bosons or fermions did not involve the full Hilbert space of the bosonized theory.
		The same thing is true in the nonabelian case.
		In this expression we observe a nonabelian version of the projective properties of the bosonized theory in the Hilbert space of all rotational wave functions.
	www.physik.fu-berlin.de /~kleinert/kleiner_re239/node21.html (642 words)

	Not Even Wrong » Blog Archive » Langlands Program and Physics (Site not responding. Last check: 2007-10-22)
		The ${SL}(2,Z)$ symmetry of abelian YM follows (at least classically obviously) from realizing it as a toroidal compactification of the theory of an abelian 2-form with self-dual field strength in six dimensions, where the ${SL}(2,Z)$ is just the modular group of the internal torus.
		The existence of that nonabelian 2-holonomy seems to be, apart from the self-duality of $H$, a further important condition on whatever Witten may mean by nonabelian gerbe field theory:
		Therefore, in order to understand nonabelian theories in 6D (and, incidentally, the general configuration of the fundamental objects of M-theory) it would be very helpful to have a notion of nonabelian surface holonomy ${hol}_{\partial V}(B)$ that makes the above expression well-defined.
	www.math.columbia.edu /~woit/blog/archives/000122.html (4262 words)

	Groups of small order.
		All groups of prime order p are isomorphic to C_p, the cyclic group of order p.
		A concrete realization of this group is Z_p, the integers under addition modulo p.
		This is the Galois group of x^5 -2 over the rationals, and can be represented as the subgroup of S_5 generated by (2 3 5 4) and (1 2 3 4 5).
	www.math.usf.edu /~eclark/algctlg/small_groups.html (1543 words)

	A Nonabelian Fundamental Group (Site not responding. Last check: 2007-10-22)
		Therefore the fundamental group of the punctured torus is nonabelian.
		In this case, h is the loop that runs all the way around the inside of the tire and returns to c.
		I'm not sure how to do this, based on the theorems we have developed thus far, but if you try to slide f around with c fixed, I think you'll see that it can't be done.
	www.mathreference.com /at,nab.html (350 words)

	ABSTRACT ALGEBRA: OnLine Study Guide, §7.6 Solved Problems
		Let p be a prime and let G be a nonabelian group of order p
		Show that the center Z(G) of G equals the commutator subgroup G' of G. Solution: Since G is nonabelian, by Exercise 7.2.13 of the text we have Z(G)
		Using the fact that the smallest simple nonabelian group has order 60, we see that the factor G/N must be simple, since otherwise each composition factor would be abelian and G would be solvable.
	www.math.niu.edu /~beachy/abstract_algebra/study_guide/soln76.html (323 words)

	Physics Help and Math Help - Physics Forums - Nonabelian self-duality
		that it is not clear that in the nonabelian case the self-duality should
		It is not clear at all that this remains true in general for nonabelian
		The existence of that nonabelian 2-holonomy seems to be, apart from the
	www.physicsforums.com /printthread.php?t=56861 (1832 words)

	A Remark on the Essential Range of Nonabelian Cocycles (ResearchIndex)
		A Remark on the Essential Range of Nonabelian Cocycles
		Abstract: We show that the essential range of a nonabelian cocycle is in general not invariant under cocycle cohomology.
		7.1%: The Essential Range of a Nonabelian Cocycle is Not a..
	citeseer.ist.psu.edu /41069.html (443 words)

	Tech Report: HPL-96-97: Hadamard Difference Sets in (Site not responding. Last check: 2007-10-22)
		In the abelian case, the exponent of the group completely determines whether the group supports a Hadamard difference set.
		Recently, a nonabelian example was constructed which exceeded the (abelian) exponent bound.
		This paper extends that result to demonstrate that the asymptotic behavior of nonabelian groups is different than that of abelian groups.
	www.hpl.hp.com /techreports/96/HPL-96-97.html (103 words)

	Generalized Quantum Mechanics of Nonabelian Gauge Theories (ResearchIndex)
		Generalized Quantum Mechanics of Nonabelian Gauge Theories (1995)
		Abstract: Hartle's generalized quantum mechanics in the sum-over-histories formalism is used to describe a nonabelian gauge theory.
		Predictions are made for certain alternatives, with particular attention given to coarse-grainings involving the constraint.
	citeseer.ist.psu.edu /whelan95generalized.html (286 words)

	John Preskill (Caltech), Topological quantum computing for beginners
		A two-dimensional medium that supports abelian anyons has a topological degeneracy that can exploited for robust storage of quantum information.
		A system of n nonabelian anyons in two-dimensions has an exponentially large topologically protected Hilbert space, and quantum information can be processed by braiding the anyons.
		I will discuss in detail two cases where nonabelian anyons can simulate a quantum circuit efficiently: fluxons in a "nonabelian superconductor," and "Fibonacci anyons" with especially simple fusion rules.
	online.kitp.ucsb.edu /online/exotic_c04/preskill (155 words)

	UC Berkeley Mathematics (Site not responding. Last check: 2007-10-22)
		I will begin by reviewing ordinary Hodge theory, which gives an equivalence between deRham and Dolbeault cohomology by ﬁnding harmonic representatives for each class.
		Then I will explain the sense in which the nonabelian Hodge theorem generalizes this picture, emphasizing the already nontrivial case of rank 1 bundles on a curve.
		The purpose of this talk will be to give a broad idea of how the abelian and nonabelian theories ﬁt together; no proofs will be given.
	math.berkeley.edu /calendar-event74.html (111 words)

	Nichols algebras of nonabelian group type (Site not responding. Last check: 2007-10-22)
		I decided to do the same thing, so here is my own zoo.
		It's kind of esoteric, but certainly nice: finite dimensional Nichols algebras over braided vector spaces of nonabelian group type.
		So here are all examples I know about of finite dimensional Nichols algebras of nonabelian group type (here by "nonabelian group type" we mean that the braided vector space does not live in a category of modules over the Drinfeld double of an abelian group).
	mate.dm.uba.ar /~matiasg/zoo.html (1154 words)

	On nonabelian local reciprocity maps, by Ivan Fesenko (Site not responding. Last check: 2007-10-22)
		On nonabelian local reciprocity maps, by Ivan Fesenko
		This paper has now appeared in Class Field Theory -- Its Centenary and Prospect (ed.
		Abelian and metabelian class field theories follow as partial cases.
	www.math.uiuc.edu /Algebraic-Number-Theory/0131 (110 words)

	Luise-Charlotte Kappe, Home Page (Site not responding. Last check: 2007-10-22)
		Thesis: Metacyclic Groups and their Nonabelian Tensor Squares
		Thesis: On Two-Generator Groups of Nilpotency Class Two and their Nonabelian Tensor Squares
		Thesis: The Nonabelian Tensor Square and Powers of a Group
	www.math.binghamton.edu /menger (63 words)

	MSC2000
		11R39 - Langlands-Weil conjectures, nonabelian class field theory[See also 11Fxx, 22E55] [
		11S37 - Langlands-Weil conjectures, nonabelian class field theory[See also 11Fxx, 22E50] [
		11R39 - Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55] [
	www.zblmath.fiz-karlsruhe.de /MATH/text/msc/view?section=11Fxx (281 words)

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