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In 1987, the Centre for Mathematical Analysis ran a Special Year on Harmonic Analysis and Operator Algebras. Most of the activity involved was concentrated in that period from May to August, and in November and December; during this time the Centre was overrun with people with disparate interests, ranging through classical Harmonic Analysis, Representation Theory, Operator Algebras, Ergodic Theory, Number Theory, Non-commutative Topology, and Mathematical Physics; at the same time, the Centre's usual program in Partial Differential Equations, Functional Analysis and Numerical Analysis was under way. Space was a problem, but this had its positive aspects too, as persons with different interests, thrown together by fate in the same office, ended up chatting with each other. Apart from informal discussions and regular and spontaneous seminars, two mini-conferences were held in the May to August period, in the (forlorn) hope that all the visitors would get a chance to speak at one or the other of these, if not both. This is the result of the first of these mini-conferences.
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Lie algebras --- Vertex operator algebras --- Group theory --- Mathematical physics --- Algebras, Vertex operator --- Operator algebras
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This book was originally published in 2006. Moonshine forms a way of explaining the mysterious connection between the monster finite group and modular functions from classical number theory. The theory has evolved to describe the relationship between finite groups, modular forms and vertex operator algebras. Moonshine Beyond the Monster describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between mathematics and mathematical physics. Written in a clear and pedagogical style, this book is ideal for graduate students and researchers working in areas such as conformal field theory, string theory, algebra, number theory, geometry and functional analysis. Containing over a hundred exercises, it is also a suitable textbook for graduate courses on Moonshine and as supplementary reading for courses on conformal field theory and string theory.
Mathematical physics. --- Finite groups. --- Finite groups --- Modular functions. --- Modular functions --- Vertex operator algebras. --- Vertex operator algebras
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Subfactors have been a subject of considerable research activity for about fifteen years and are known to have significant relations with other fields such as low dimensional topology and algebraic quantum field theory. These notes give an introduction to the subject suitable for a student who has only a little familiarity with the theory of Hilbert space. A new pictorial approach to subfactors is presented in a late chapter.
Operator algebras. --- Algebras, Operator --- Operator theory --- Topological algebras
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Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas.This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly e
Operator algebras. --- Representations of algebras. --- Algèbres d'opérateurs --- Représentations d'algèbres --- Operator algebras --- Representations of algebras --- Algebra --- Algebras, Operator --- Operator theory --- Topological algebras
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Fundamentals of the theory of operator algebras. V4
Operator algebras. --- Operator theory. --- Functional analysis --- Algebras, Operator --- Operator theory --- Topological algebras
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Fundamentals of the theory of operator algebras. V2
Operator algebras. --- Linear operators. --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory --- Algebras, Operator --- Topological algebras
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Free Probability Theory studies a special class of 'noncommutative'random variables, which appear in the context of operators on Hilbert spaces and in one of the large random matrices. Since its emergence in the 1980s, free probability has evolved into an established field of mathematics with strong connections to other mathematical areas, such as operator algebras, classical probability theory, random matrices, combinatorics, representation theory of symmetric groups. Free probability also connects to more applied scientific fields, such as wireless communication in electrical engineering. This 2006 book gives a self-contained and comprehensive introduction to free probability theory which has its main focus on the combinatorial aspects. The volume is designed so that it can be used as a text for an introductory course (on an advanced undergraduate or beginning graduate level), and is also well-suited for the individual study of free probability.
Combinatorial analysis. --- Free probability theory. --- Probability theory, Free --- Operator algebras --- Selfadjoint operators --- Combinatorics --- Algebra --- Mathematical analysis
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The theory of operator algebras is generally considered over the field of complex numbers and in the complex Hilbert spaces. So it is a natural and interesting problem: How is the theory in the field of real numbers? Up to now, the theory of operator algebras over the field of real numbers has seemed not to be introduced systematically and sufficiently.The aim of this book is to set up the fundamentals of real operator algebras and to give a systematic discussion for real operator algebras. Since the treatment is from the beginning (real Banach and Hilbert spaces, real Banach algebras, real Ba
Banach algebras. --- Operator algebras. --- Algebras, Operator --- Operator theory --- Topological algebras --- Algebras, Banach --- Banach rings --- Metric rings --- Normed rings --- Banach spaces
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This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory. Sample Chapter(s)
A Walk in the Noncommutative Garden (1,639 KB)
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