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Topic: Von Neumann algebras

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	[No title]
		Von Neumann algebras, traces and von Neumann dimensions.
		Von Neumann algebras and traces associated with actions of discrete groups on manifolds.
		Tensor producst of von Neumann algebras and traces.
	www.math.neu.edu /grad/semconv/VonNeumann.doc (307 words)

	Quantum Theory: von Neumann vs. Dirac (Stanford Encyclopedia of Philosophy)
		A von Neumann algebra is a factor, if its center (which is the set of elements that commute with all elements of the algebra) is trivial, meaning that each of its elements is a scalar times the identity element.
		In algebraic quantum field theory, an algebra of observables is associated with bounded regions of Minkowski spacetime (and unbounded regions including all of spacetime by way of certain limiting operations) that are required to satisfy standard axioms of local structure: isotony, locality, covariance, additivity, positive spectrum, and a unique invariant vacuum state.
		In algebraic quantum field theory the predominant view is that a continuum of inequivalent representations constitutes an embarrassment; it is sometimes mitigated by appending a pragmatic twist to the effect that one should simply choose the most convenient representation for the purpose at hand.
	plato.stanford.edu /entries/qt-nvd (10281 words)

	Research
		Von Neumann algebras are algebras M of operators on a Hilbert space H closed in the strong topology.
		This dual characterization, one analytic and one algebraic is at the heart of the rich structure and broad influence that the study of von Neumann algebras has produced.
		All von Neumann algebras can be realized as a direct sum (or a direct integral) of factors and thus the study of von Neumann algebras can be refined to the study of factors.
	www.sci.ccny.cuny.edu /~landau/wp3.html (1051 words)

	Von Neumann
		Von Neumann contributed to “automata theory” and then became involved in a mixture of pure and applied mathematics.
		During the second World War von Neumann was instrumental in proposing implosion as a method of bringing nuclear fuel to explosion and thereafter contributed to the development of the hydrogen bomb.
		In 1929 von Neumann was invited to become a member of the Princeton faculty and therefore escaped the Nazi persecutions soon to follow.
	www.jbuff.com /c090403.htm (764 words)

	MGSO Home Page (via CobWeb/3.1 planetlab1.isi.jhu.edu) (Site not responding. Last check: 2007-11-06)
		von Neumann algebras were named for John von Neumann and are *-algebras of bounded operators on a Hilbert space that are closed in the weak operator topology and contain the identity operator.
		A von Neumann algebra whose center consists only of multiples of the identity operator is called a factor.
		Every von Neumann algebra on a separable Hilbert space is isomorphic to a direct integral of factors and this decomposition is essentially unique.
	mosaic.math.tamu.edu.cob-web.org:8888 (152 words)

	hyperfinite II1 von Neumann algebra Clifford algebra
		Every von Neumann algebra can be built from so-called "simple" ones as a direct sum, or more generally a "direct integral", which is a kind of continuous version of a direct sum.
		The Clifford algebra is the simplest of the factors that are direct limits of matrix algebras...".
		[a factor of a von Neumann algebra is a] von Neumann algebra...
	www.valdostamuseum.org /hamsmith/II1vNfactor.html (3539 words)

	articles28.htm
		Von Neumann algebras are weakly closed -subalgebras of the algebra* of all bounded operators on a Hilbert space.
		But finite dimensional von Neumann algebras are nothing but direct sums of full matrix algebras and their inclusions can be described through certain graphs known as Brattelli diagrams.
		It is clear that the authors have assumed that the reader is familiar with basics of operator algebra theory on Hilbert spaces; for instance, the introduction to von Neumann algebras given is a little too brief.
	www.ias.ac.in /currsci/nov10/articles28.htm (843 words)

	06w5086 Topics on von Neumann algebras (via CobWeb/3.1 planetlab1.isi.jhu.edu) (Site not responding. Last check: 2007-11-06)
		Von Neumann algebras are algebras of bounded linear operators on a Hilbert space which are closed under the topology of pointwise convergence.
		Von Neumann algebras were first studied in a series of papers by Murray and von Neumann in the 1930's.
		In fact, since the special year on operator algebras at MSRI in 2000/2001, there was only one such meeting earlier this year at CIRM, Marseille, France in which specialists in von Neumann algebras met with experts in group theory and topology.
	www.pims.math.ca.cob-web.org:8888 /birs/birspages.php?task=displayevent&event_id=06w5086 (1686 words)

	[No title]
		A von Neumann algebra is an involutive subalgebra $A$ of $B(H)$ which is closed in the weak topology on $B(H)$.
		This algebra is in a natural sense a "direct integral" of copies of ${\bf C}$, which is a factor---that is, a von Neumann algebra with trivial centre.
		There are remarkable links between this von Neumann algebra and the more classical invariants of foliations, for example the result (originally due to Steve Hurder) that if the Godbillon-Vey class of a foliation is nonzero, then the associated von Neumann algebra is of type III.
	www.math.niu.edu /~rusin/known-math/98/knots_n_FA (3215 words)

	Crossed products of operator algebras and Fell buindles over equivalence relations
		In the case of von Neumann algebras, such a construction was introduced by Feldman and Moore [3,4] in 1977, in the case of C* -algebras --- it was introduced by Renault [13] in 1980.
		The results concerning von Neumann algebras are submitted to publication, and the article should appear in May 1997 (see [6]).
		The algebra D is to be generated by a continuous field of C* -algebras.
	math.la.asu.edu /~ifulman/report/report.html (986 words)

	A Survey of Operator Algebras
		Motivated by quantum mechanics and group representation theory, John von Neumann introduced in the early 30's certain algebras of bounded operators on a Hilbert space, the so-called von Neumann algebras.
		Dan Voiculescu's free probability theory introduced probabilistic methods to the analysis of von Neumann algebras associated to free groups and his new concept of free entropy can be viewed as a measure of freeness in this context.
		In 1980, von Klitzing showed that the Hall conductivity of a disordered crystal is quantized and in 1985 he won the Nobel prize in Physics (at the age of 42) for this discovery.
	www.math.wm.edu /~tomforde/opsurvey.html (723 words)

	Operator Algebras (Site not responding. Last check: 2007-11-06)
		In von Neumann algebra theory, the research currently is mostly devoted to free probability theory, but the research also covers classification of factors, and Jones subfactor theory.
		The research group in Odense is part of a larger Danish group of scientists in operator algebras from three Danish universities (Copenhagen, Aarhus and Odense).
		The group is organizing a conference Operator Algebras and Applications to be held April 2006.
	www.imada.sdu.dk /Research/operator_algebras.php (276 words)

	Elementary theory of von Neumann algebras (via CobWeb/3.1 planetlab1.isi.jhu.edu) (Site not responding. Last check: 2007-11-06)
		The algebras in the title were introduced in the 1930'ies by Murray and von Neumann.
		By definition, the von Neumann algebras are certain algebras of operators acting on a Hilbert space.
		In particular, we will separate von Neumann algebras into (algebraically non-isomorphic) types and show that each such algebra is a direct sum of algebras of various types.
	www.imf.au.dk.cob-web.org:8888 /da/uddannelse/beskrivelser/older/F1996-F1998/node152.html (186 words)

	hyhperfinite II1 von Neumann algebra Clifford algebra
		A von Neumann algebra of "localised observables" is postulated for each bounded region of space-time.
		Causality implies that these von Neumann algebras commute with each other if no physical signal can travel between the regions in which they are localised.
		Using actions of free groups it is easy to construct families of subfactors with the same standard invariant, and an unpublished result of Popa implies that even the simplest case (the "Temperley-Lieb" algebra in planar algebra terminology) is not always obtainable from a hyperfinite subfactor.
	www.valdostamuseum.org /hamsmith/ClifTensorGeom.html (2483 words)

	NCGOA Seminar, Spring 2004
		The result we present is the computation of Free Entropy of the group von Neumann algebra associated to the special linear group SL(Z, 2n+1).
		After that we will show that this von Neumann algebra is generated by two selfadjoint operators, which settles a problem proposed by Voiculescu.
		Abstract: In the 1940's, Hochschild introduced cohomology groups for algebras, and these were adapted by Kadison and Ringrose in the 1970's to the functional analytic setting of von Neumann algebras, the weakly closed self-adjoint subalgebras of bounded operators on a Hilbert space.
	www.math.vanderbilt.edu /~bisch/NCGOA_seminar_spring04.html (1461 words)

	CJM - Correspondences, von Neumann Algebras and Holomorphic L² Torsion
		CJM - Correspondences, von Neumann Algebras and Holomorphic L
		Given a holomorphic Hilbertian bundle on a compact complex manifold, we introduce the notion of holomorphic $L^2$ torsion, which lies in the determinant line of the twisted $L^2$ Dolbeault cohomology and represents a volume element there.
		We therefore initiate the theory of correspondences of determinant lines, that enables us to define a relative holomorphic $L^2$ torsion for a pair of flat Hilbertian bundles, which we prove is independent of the choice of Hermitian metrics on the complex manifold and on the flat Hilbertian bundles.
	journals.cms.math.ca /cgi-bin/vault/view/carey1062 (193 words)

	Topics in advanced theory of von Neumann algebras (via CobWeb/3.1 planetlab1.isi.jhu.edu) (Site not responding. Last check: 2007-11-06)
		This is a continuation of the course on elementary theory of von Neuman algebras.
		The Tomita-Takesaki theory describes the relation between a von Neumann algebra and its commutant under certain conditions.
		The theory is a far-reaching tool to study further structure of von Neumann algebras.
	www.imf.au.dk.cob-web.org:8888 /da/uddannelse/beskrivelser/older/F1996-F1998/node135.html (156 words)

	Uffe Haagerup (Site not responding. Last check: 2007-11-06)
		Haagerup and E. Størmer, Positive projections of von Neumann algebras onto JW-algebras, Proceedings of the XXVII Symposium on Mathematical Physics, Torun 1994, Rep. Math.
		Haagerup and C. Winsløw, The Effros-Mareshal topology in the space of von Neumann algebras, Amer.
		Haagerup and C. Winsløw, The Effros-Mareshall topology in the space of von Neumann algebras II, preprint (28 pp.), Copenhagen 1998.
	www.imada.sdu.dk /~haagerup/?show=all (1349 words)

	Math 468 - Basic Theory of von Neumann Algebras (Site not responding. Last check: 2007-11-06)
		It should be apparent (and perhaps a little intimidating) that the study of von Neumann algebras requires analysis and algebra both, with operator theory at the interface.
		It is foundational, if not central, for the subject of operator algebras, which has brought new perspectives to nearly every area of mathematics.
		Probably this will be somewhat open-ended; instead of simply solving a problem, students will be encouraged to look over the literature and report on a theme or unsolved problem.
	www.math.uiuc.edu /~dasherma/468/syllabus.html (392 words)

	C -algebra von Neumann algebras complex adjoint quantum mechanics contractive isomorphic compact operator quotient ... (Site not responding. Last check: 2007-11-06)
		» -algebras were first considered primarily for their use in quantum mechanics to model algebras of physical observables.
		Subsequently John von Neumann attempted to establish a general framework for these algebras which culminated in a series of papers on rings of operators.
		K(H) is the algebra of compact operators on H.
	en.powerwissen.com.cob-web.org:8888 /o2gIlKhfgVrXlNBMn18uwg==_C_-algebra.html (1264 words)

	Abstract of: A bicategorical approach to Morita equivalence for von Neumann algebras (Site not responding. Last check: 2007-11-06)
		Abstract of: A bicategorical approach to Morita equivalence for von Neumann algebras
		We relate Morita equivalence for von Neumann algebras to the ``Connes fusion'' tensor product between correspondences.
		We present a similar result for von Neumann algebras.
	db.cwi.nl /rapporten/abstract.php?abstractnr=1341 (141 words)

	publ
		Petz, A characterization of the canonical centre-valued trace in finite von Neumann algebras:
		Petz, Quasi-uniform ergodic theorems in von Neumann algebras:
		Petz, Sufficient subalgebras and the relative entropy of states of a von Neumann algebra:
	www.math-inst.hu /~petz/publ.html (1320 words)

	AMCA: Applying Torsion Theories to Finite von Neumann algebras by Lia Vas (Site not responding. Last check: 2007-11-06)
		AMCA: Applying Torsion Theories to Finite von Neumann algebras by Lia Vas
		Von Neumann algebras facilitate the study of certain topological spaces.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/j/u/81.htm (93 words)

	Re: W*-algebras (aka von Neumann algebras)
		It's >not usually true that L(X) is isomorphic to L(R(L(X))) for a Lie >algebra X. Typically, each time we go back and forth using L and >R, our gadget gets bigger.
		I took the class at the University of Nebraska, where, unlike at Caltech, you need the instructor's permission if you want to take a graduate level course while an undergrad.
		As it turned out, I had zero trouble getting into either course, but I was paranoid enough to make sure I got every single problem right, so I learned those preliminaries very well.
	www.lns.cornell.edu /spr/2000-02/msg0022461.html (826 words)

	AMCA: Decomposability of von Neumann algebras associated with locally compact groups by Matthias Neufang (Site not responding. Last check: 2007-11-06)
		The decomposability number of a von Neumann algebra M, denoted by dec(M), is defined to be the greatest cardinality of a family of pairwise orthogonal, non-zero projections in M. This is a very natural invariant since a von Neumann algebra is determined by its projections.
		In this talk, I shall focus on those von Neumann algebras whose preduals are function spaces/Banach algebras on a locally compact group G, such as the group algebra L
		I shall present applications reaching from semigroup compactifications over the topological center problem to Kac algebras.
	at.yorku.ca /c/a/l/v/03.htm (207 words)

	On the tensor products of von Neumann algebras., Jun Tomiyama
		On the tensor products of von Neumann algebras.
		[1] J. Hakeda and J. Tomiyama, On some extension properties of von Neumann algebras, Thoku Math.
		[8] M. Tomita, Standard forms of von Neumann algebras (to appear)
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.pjm/1102978713 (190 words)

	Classification of essential commutants of abelian von Neumann algebras., Bruce H. Wagner
		Classification of essential commutants of abelian von Neumann algebras., Bruce H. Wagner
		Classification of essential commutants of abelian von Neumann algebras.
		[JP] B. Johnson and S. Parrott, Operatorscommuting with a von Neumann algebramodulo theset of compact operators,J. Funct.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.pjm/1102644469 (183 words)

	algebras (Site not responding. Last check: 2007-11-06)
		von Neumann algebras, volume 27 of North-Holland Mathematical Library.
		Reprint of the first (1979) edition, Operator Algebras and Non-commutative Geometry, 5.
		This file has been generated by bibtex2html 1.66
	www.princeton.edu /~hhalvors/teaching/phi538_s2004/algebras.html (115 words)

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