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15
The geometry of dynamical triangulations
 Lecture Notes in Physics m50
, 1997
"... The express purpose of these Lecture Notes is to go through some aspects of the simplicial quantum gravity model known as the Dynamical Triangulations approach. Emphasis has been on lying the foundations of the theory and on illustrating its subtle and often unexplored connections with many distinct ..."
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Cited by 35 (3 self)
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The express purpose of these Lecture Notes is to go through some aspects of the simplicial quantum gravity model known as the Dynamical Triangulations approach. Emphasis has been on lying the foundations of the theory and on illustrating its subtle and often unexplored connections with many distinct mathematical fields ranging from global riemannian geometry, moduli theory, number theory, and topology. Our exposition will concentrate on these points so that graduate students may find in these notes a useful exposition of some of the rigorous results one can establish in this field and hopefully a source of inspiration for new exciting problems. We also illustrate the deep and beautiful interplay between the analytical aspects of dynamical triangulations and the results of MonteCarlo simulations. The techniques described here are rather novel and allow us to address successfully many high points of great current interest in the subject of simplicial quantum gravity while requiring very lit1 tle in the way of fancy field theoretical arguments. As a consequence, these
TRIPLES, ALGEBRAS AND COHOMOLOGY
 REPRINTS IN THEORY AND APPLICATIONS OF CATEGORIES
, 2003
"... ..."
Nonassociative tori and applications to Tduality
 hepth/0412092. TDUALITY VIA NONCOMMUTATIVE TOPOLOGY
"... Abstract. In this paper, we initiate the study of C ∗algebras A endowed with a twisted action of a locally compact Abelian Lie group G, and we construct a twisted crossed product A⋊G, which is in general a nonassociative, noncommutative, algebra. The duality properties of this twisted crossed produ ..."
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Cited by 29 (7 self)
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Abstract. In this paper, we initiate the study of C ∗algebras A endowed with a twisted action of a locally compact Abelian Lie group G, and we construct a twisted crossed product A⋊G, which is in general a nonassociative, noncommutative, algebra. The duality properties of this twisted crossed product algebra are studied in detail, and are applied to Tduality in Type II string theory to obtain the Tdual of a general principal torus bundle with general Hflux, which we will argue to be a bundle of noncommutative, nonassociative tori. We also show that this construction of the Tdual includes all of the special cases that were previously analysed. 1.
Solvable groups definable in ominimal structures
 J. Pure Appl. Algebra
, 2003
"... Let N be an ominimal structure. In this paper we develop group extension theory over N and use it to describe Ndefinable solvable groups. We prove an ominimal analogue of the LieKolchinMal’cev theorem and we describe Ndefinable Gmodules and Ndefinable rings. 1 1 ..."
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Cited by 10 (3 self)
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Let N be an ominimal structure. In this paper we develop group extension theory over N and use it to describe Ndefinable solvable groups. We prove an ominimal analogue of the LieKolchinMal’cev theorem and we describe Ndefinable Gmodules and Ndefinable rings. 1 1
R.: Obstruction theory for extensions of categorical groups
 Appl. Categ. Structures
"... Abstract. For any categorical group H, we introduce the categorical group Out(H) andthenthe wellknown group exact sequence 1 → Z(H) → H → Aut(H) → Out(H) → 1israisedtoa categorical group level by using a suitable notion of exactness. Breen’s Schreier theory for extensions of categorical groups i ..."
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Cited by 5 (4 self)
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Abstract. For any categorical group H, we introduce the categorical group Out(H) andthenthe wellknown group exact sequence 1 → Z(H) → H → Aut(H) → Out(H) → 1israisedtoa categorical group level by using a suitable notion of exactness. Breen’s Schreier theory for extensions of categorical groups is codified in terms of homomorphism to Out(H) and then we develop a sort of Eilenberg–Mac Lane obstruction theory that solves the general problem of the classification of all categorical group extensions of a group G by a categorical group H, in terms of ordinary group cohomology.
Discrete random electromagnetic Laplacians
 in the Mathematical Physics Preprint Archive, mp arc@math.utexas.edu
, 1995
"... We consider discrete random magnetic Laplacians in the plane and discrete random electromagnetic Laplacians in higher dimensions. The existence of these objects relies on a theorem of FeldmanMoore which was generalized by Lind to the nonabelian case. For example, it allows to realize ergodic Schrod ..."
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Cited by 5 (4 self)
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We consider discrete random magnetic Laplacians in the plane and discrete random electromagnetic Laplacians in higher dimensions. The existence of these objects relies on a theorem of FeldmanMoore which was generalized by Lind to the nonabelian case. For example, it allows to realize ergodic Schrodinger operators with stationary independent magnetic fields on discrete two dimensional lattices including also nonperiodic situations like Penrose lattices. The theorem is generalized here to higher dimensions. The Laplacians obtained from the electromagnetic vector potential are elements of a von Neumann algebra constructed from the underlying dynamical system respectively from the ergodic equivalence relation. They generalize Harper operators which correspond to constant magnetic fields. For independent identically distributed magnetic fields and special Anderson models, we compute the density of states using a random walk expansion. Mathematics subject classification: 28D15, 47A10, 47A3...
A.: Graded extensions of monoidal categories
 J. Algebra
"... The longknown results of Schreier�Eilenberg�Mac Lane on group extensions are raised to a categorical level, for the classification and construction of the manifold of all graded monoidal categories, the type being given group � with 1component a given monoidal category. Explicit application is mad ..."
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Cited by 4 (3 self)
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The longknown results of Schreier�Eilenberg�Mac Lane on group extensions are raised to a categorical level, for the classification and construction of the manifold of all graded monoidal categories, the type being given group � with 1component a given monoidal category. Explicit application is made to the classification of strongly graded bialgebras over commutative rings. � 2001 Academic Press
AND EXAMPLES
, 2009
"... Abstract. In this last article of the series on outer actions of a countable discrete amenable group on AFD factors, we analyze outer actions of a countable discrete free abelian group on an AFD factor of type IIIλ, 0 < λ < 1, and compute outer conjugacy invariants. As a byproduct, we discover the a ..."
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Abstract. In this last article of the series on outer actions of a countable discrete amenable group on AFD factors, we analyze outer actions of a countable discrete free abelian group on an AFD factor of type IIIλ, 0 < λ < 1, and compute outer conjugacy invariants. As a byproduct, we discover the asymmetrization technique for coboundary condition on a Tvalued cocycle of a torsion free abelian group, which might have been known by the group cohomologists. As the asymmetrization technique gives us a very handy criteria for coboundaries, we present it here in detail in the second section. Contents §0. Introduction. §1. Simple examples and model construction.