Groups and group theory

This monograph introduces and explores the notions of a commutator equation and the equationally-defined commutator from the perspective of abstract algebraic logic.

This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role.

This book presents a graduate-level course on modern algebra.

Written by one of the subject's foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist.

This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture.

This is a textbook that derives the fundamental theories of physics from symmetry.

This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing.

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This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach.

This book gathers peer-reviewed contributions representing modern trends in the theory of generalized functions and pseudo-differential operators.

This collection of surveys and research articles explores a fascinating class of varieties: Beauville surfaces.

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites.

Providing a nearly complete selection of up-to-date methods and results on block invariants with respect to their defect groups, this book covers the classical theory pioneered by Brauer, the modern theory of fusion systems introduced by Puig, the geometry of numbers developed by Minkowski, the classification of finite simple groups, and various computer assisted methods.

This edited volume presents a collection of carefully refereed articles covering the latest advances in Automorphic Forms and Number Theory, that were primarily developed from presentations given at the 2012 "e;International Conference on Automorphic Forms and Number Theory,"e; held in Muscat, Sultanate of Oman.

We present an introduction to Berkovich's theory of non-archimedean analytic spaces that emphasizes its applications in various fields.

This short book provides a comprehensive and unified treatment of time-varying vector fields under a variety of regularity hypotheses, namely finitely differentiable, Lipschitz, smooth, holomorphic, and real analytic.

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades.

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades.

Hypercomplex analysis is the extension of complex analysis to higher dimensions where the concept of a holomorphic function is substituted by the concept of a monogenic function.

In mathematical physics, the correspondence between quantum and classical mechanics is a central topic, which this book explores in more detail in the particular context of spin systems, that is, SU(2)-symmetric mechanical systems.

The Farrell-Jones isomorphism conjecture in algebraic K-theory offers a description of the algebraic K-theory of a group using a generalized homology theory.

Combinatorial Algebra: Syntax and Semantics provides comprehensive account of many areas of combinatorial algebra.

Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory.

Probability theory on compact Lie groups deals with the interaction between "e;chance"e; and "e;symmetry,"e; a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing).

Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains only two places.

This volume features seventeen extended conference abstracts corresponding to selected talks given by participants at the CRM research program "e;Automorphisms of Free Groups: Algorithms, Geometry and Dynamics"e;, which took place at the Centre de Recerca Matematica in Barcelona in fall 2012.

The main focus of this thesis is the mathematical structure of Group Field Theories (GFTs) from the point of view of renormalization theory.

The Bialowieza Workshops on Geometric Methods in Physics, which are hosted in the unique setting of the Bialowieza natural forest in Poland, are among the most important meetings in the field.

Descriptive topology and functional analysis, with extensive material demonstrating new connections between them, are the subject of the first section of this work.

For most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research.

This book takes the reader on a mathematical journey, from a number-theoretic point of view, to the realm of Markov's theorem and the uniqueness conjecture, gradually unfolding many beautiful connections until everything falls into place in the proof of Markov's theorem.

This manuscript is devoted to classifying the isomorphism classes of the virtually cyclic subgroups of the braid groups of the 2-sphere.

This book describes the endeavour to relate the particle spectrum with representations of operational electroweak spacetime, in analogy to the atomic spectrum as characterizing representations of hyperbolic space.

This book explains the group representation theory for quantum theory in the language of quantum theory.

The purpose of this monograph is to provide a theory of Markov processes that are invariant under the actions of Lie groups, focusing on ways to represent such processes in the spirit of the classical Levy-Khinchin representation.