Noncommutative Coordinates for Symplectic Representations
Author: Daniele Alessandrini
Publisher: American Mathematical Society
Published: 2024-09-09
Total Pages: 130
ISBN-13: 1470471086
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In the Tradition of Thurston II
Author: Ken’ichi Ohshika
Publisher: Springer Nature
Published: 2022-08-02
Total Pages: 525
ISBN-13: 3030975606
DOWNLOAD EBOOKThe purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston’s heritage. Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The topics covered in the present volume include com-plex hyperbolic Kleinian groups, Möbius structures, hyperbolic ends, cone 3-manifolds, Thurston’s norm, surgeries in representation varieties, triangulations, spaces of polygo-nal decompositions and of singular flat structures on surfaces, combination theorems in the theories of Kleinian groups, hyperbolic groups and holomorphic dynamics, the dynamics and iteration of rational maps, automatic groups, and the combinatorics of right-angled Artin groups.
Noncommutative Coordinates for Symplectic Representations
Author: Daniele Alessandrini
Publisher:
Published: 2024
Total Pages: 0
ISBN-13: 9781470471088
DOWNLOAD EBOOKWe introduce coordinates on the spaces of framed and decorated representations of the fundamental group of a surface with nonempty boundary into the symplectic group Sp(2n, R). These coordinates provide a noncommutative generalization of the parametrizations of the spaces of representations into SL(2, R) or PSL(2, R) given by Thurston, Penner, Kashaev and Fock–Goncharov. On the space of decorated symplectic representations the coordinates give a geometric realization of the noncommutative cluster-like structures introduced by Berenstein–Retakh. The locus of positive coordinates maps to the space of framed maximal representations. We use this to determine an explicit homeomorphism between the space of framed maximal representations and a quotient by the group O(n). This allows us to describe the homotopy type and, when n=2, to give an exact description of the singularities. Along the way, we establish a complete classification of pairs of nondegenerate quadratic forms.
Representation Theory and Noncommutative Harmonic Analysis I
Author: A.A. Kirillov
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 241
ISBN-13: 3662030020
DOWNLOAD EBOOKThis two-part survey provides a short review of the classical part of representation theory, carefully exposing the structure of the theory without overwhelming readers with details, and deals with representations of Virasoro and Kac-Moody algebra. It presents a wealth of recent results on representations of infinite-dimensional groups.
Geometric Models for Noncommutative Algebras
Author: Ana Cannas da Silva
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 202
ISBN-13: 9780821809525
DOWNLOAD EBOOKThe volume is based on a course, ``Geometric Models for Noncommutative Algebras'' taught by Professor Weinstein at Berkeley. Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, for example, the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces. In this work, the authors discuss several types of geometric objects (in the usual sense of sets with structure) that are closely related to noncommutative algebras. Central to the discussion are symplectic and Poisson manifolds, which arise when noncommutative algebras are obtained by deforming commutative algebras. The authors also give a detailed study of groupoids (whose role in noncommutative geometry has been stressed by Connes) as well as of Lie algebroids, the infinitesimal approximations to differentiable groupoids. Featured are many interesting examples, applications, and exercises. The book starts with basic definitions and builds to (still) open questions. It is suitable for use as a graduate text. An extensive bibliography and index are included.
Noncommutative Birational Geometry, Representations and Combinatorics
Author: Arkady. Berenstein
Publisher: American Mathematical Soc.
Published: 2013-05-01
Total Pages: 265
ISBN-13: 082188980X
DOWNLOAD EBOOK"This volume contains the proceedings of the AMS Special Session on Noncommutative Birational Geometry, Representations and Cluster Algebras, held from January 6-7, 2012, in Boston, MA. The papers deal with various aspects of noncommutative birational geometry and related topics, focusing mainly on structure and representations of quantum groups and algebras, braided algebras, rational series in free groups, Poisson brackets on free algebras, and related problems in combinatorics. This volume is useful for researchers and graduate students in mathematics and mathematical physics who want to be introduced to different areas of current research in the new area of noncommutative algebra and geometry."--Publisher's website.
Noncommutative Harmonic Analysis
Author: Michael Eugene Taylor
Publisher: American Mathematical Soc.
Published: 1986
Total Pages: 346
ISBN-13: 0821815237
DOWNLOAD EBOOKExplores some basic roles of Lie groups in linear analysis, with particular emphasis on the generalizations of the Fourier transform and the study of partial differential equations.
Noncommutative Geometry and Representation Theory in Mathematical Physics
Author: Jürgen Fuchs
Publisher: American Mathematical Soc.
Published: 2005
Total Pages: 402
ISBN-13: 0821837184
DOWNLOAD EBOOKMathematics provides a language in which to formulate the laws that govern nature. It is a language proven to be both powerful and effective. In the quest for a deeper understanding of the fundamental laws of physics, one is led to theories that are increasingly difficult to put to the test. In recent years, many novel questions have emerged in mathematical physics, particularly in quantum field theory. Indeed, several areas of mathematics have lately become increasingly influentialin physics and, in turn, have become influenced by developments in physics. Over the last two decades, interactions between mathematicians and physicists have increased enormously and have resulted in a fruitful cross-fertilization of the two communities. This volume contains the plenary talks fromthe international symposium on Noncommutative Geometry and Representation Theory in Mathematical Physics held at Karlstad University (Sweden) as a satellite conference to the Fourth European Congress of Mathematics. The scope of the volume is large and its content is relevant to various scientific communities interested in noncommutative geometry and representation theory. It offers a comprehensive view of the state of affairs for these two branches of mathematical physics. The book is suitablefor graduate students and researchers interested in mathematical physics.
Noncommutative Geometry
Author: Alain Connes
Publisher: Springer
Published: 2003-12-15
Total Pages: 364
ISBN-13: 3540397027
DOWNLOAD EBOOKNoncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)
Author: Boyan Sirakov
Publisher: World Scientific
Published: 2019-02-27
Total Pages: 5393
ISBN-13: 9813272899
DOWNLOAD EBOOKThe Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
