Modular Lie Algebras and their Representations

Modular Lie Algebras and their Representations
Author: H. Strade
Publisher: CRC Press
Total Pages: 318
Release: 2020-08-11
Genre: Mathematics
ISBN: 1000103390

This book presents an introduction to the structure and representation theory of modular Lie algebras over fields of positive characteristic. It introduces the beginner to the theory of modular Lie algebras and is meant to be a reference text for researchers.

Introduction to Representation Theory

Introduction to Representation Theory
Author: Pavel I. Etingof
Publisher: American Mathematical Soc.
Total Pages: 240
Release: 2011
Genre: Mathematics
ISBN: 0821853511

Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.

Modules and the Structure of Rings

Modules and the Structure of Rings
Author: Golan
Publisher: Routledge
Total Pages: 298
Release: 2017-10-19
Genre: Mathematics
ISBN: 135143036X

This textbook is designed for students with at least one solid semester of abstract algebra,some linear algebra background, and no previous knowledge of module theory. Modulesand the Structure of Rings details the use of modules over a ring as a means of consideringthe structure of the ring itself--explaining the mathematics and "inductivereasoning" used in working on ring theory challenges and emphasizing modules insteadof rings.Stressing the inductive aspect of mathematical research underlying the formal deductivestyle of the literature, this volume offers vital background on current methods for solvinghard classification problems of algebraic structures. Written in an informal butcompletely rigorous style, Modules and the Structure of Rings clarifies sophisticatedproofs ... avoids the formalism of category theory ... aids independent study or seminarwork ... and supplies end-of-chapter problems.This book serves as an excellent primary.text for upper-level undergraduate and graduatestudents in one-semester courses on ring or module theory-laying a foundation formore advanced study of homological algebra or module theory.

Continuum Theory

Continuum Theory
Author: Sam Nadler
Publisher: CRC Press
Total Pages: 349
Release: 2017-07-12
Genre: Mathematics
ISBN: 1482277166

A textbook for either a semester or year course for graduate students of mathematics who have had at least one course in topology. Introduces continuum theory through a combination of classical and modern techniques. Annotation copyright Book News, Inc. Portland, Or.

Theory of Distributions

Theory of Distributions
Author: M.A. Al-Gwaiz
Publisher: CRC Press
Total Pages: 276
Release: 1992-04-24
Genre: Mathematics
ISBN: 0849306698

A textbook for a graduate course in the theory of distributions and related topics, for students of applied mathematics or theoretical physics. Introduces the theory, explicates mathematical structures and the Hilbert-space aspects, and presents applications to typical boundary problems. Annotation

Ring Theory

Ring Theory
Author: Kenneth Goodearl
Publisher: CRC Press
Total Pages: 224
Release: 1976-03-01
Genre: Mathematics
ISBN: 9780824763541

Tensors and the Clifford Algebra

Tensors and the Clifford Algebra
Author: Alphonse Charlier
Publisher: CRC Press
Total Pages: 352
Release: 2020-08-26
Genre: Mathematics
ISBN: 1000147991

This practical reference and text presents the applications of tensors, Lie groups and algebra to Maxwell, Klein-Gordon and Dirac equations, making elementary theoretical physics comprehensible and high-level theoretical physics accessible.;Providing the fundamental mathematics necessary to understand the applications, Tensors and the Clifford Algebra offers lucid discussions of covariant tensor calculus; examines subjects from a variety of perspectives; supplies highly detailed developments of all calculations; employs the language of physics in its explanations; and illustrates the use of Clifford algebra and tensor calculus in studying bosons and fermions.;With over 2800 display equations and 14 appendixes, this book should be a useful reference for mathematical physicists and applied mathematicians, and an important text for upper-level undergraduate and graduate students in quantum mechanics, relativity, electromagnetism, theoretical physics, elasticity and field theory courses.

Incidence Algebras

Incidence Algebras
Author: Eugene Spiegel
Publisher: Routledge
Total Pages: 352
Release: 2022-01-26
Genre: Mathematics
ISBN: 1351439014

This work covers the maximal and prime ideals of the incidence algebra, derivations and isomorphisms, radicals and additional ring-theoretic properties. Combinatorial discussions include a study of the Mobius function, reduced incidence subalgebras, and the coalgebra approach to incidence algebras.