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Algebraic Groups: Structure and Actions
  • Language: en
  • Pages: 306

Algebraic Groups: Structure and Actions

This volume contains the proceedings of the 2015 Clifford Lectures on Algebraic Groups: Structures and Actions, held from March 2–5, 2015, at Tulane University, New Orleans, Louisiana. This volume consists of six articles on algebraic groups, including an enhanced exposition of the classical results of Chevalley and Rosenlicht on the structure of algebraic groups; an enhanced survey of the recently developed theory of pseudo-reductive groups; and an exposition of the recently developed operational -theory for singular varieties. In addition, there are three research articles containing previously unpublished foundational results on birational automorphism groups of algebraic varieties; sol...

Quadratic Forms, Linear Algebraic Groups, and Cohomology
  • Language: en
  • Pages: 344

Quadratic Forms, Linear Algebraic Groups, and Cohomology

Developments in Mathematics is a book series devoted to all areas of mathematics, pure and applied. The series emphasizes research monographs describing the latest advances. Edited volumes that focus on areas that have seen dramatic progress, or are of special interest, are encouraged as well.

Handbook of K-Theory
  • Language: en
  • Pages: 1148

Handbook of K-Theory

This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.

Non-Associative Algebra and Its Applications
  • Language: en
  • Pages: 558

Non-Associative Algebra and Its Applications

  • Type: Book
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  • Published: 2006-01-13
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  • Publisher: CRC Press

With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences. This book covers material such as Jordan superalgebras, nonassociative deformations, nonassociative generalization of Hopf algebras, the structure of free algebras, derivations of Lie algebras, and the identities of Albert algebra. It also includes applications of smooth quasigroups and loops to differential geometry and relativity.

Rings with Polynomial Identities and Finite Dimensional Representations of Algebras
  • Language: en
  • Pages: 645

Rings with Polynomial Identities and Finite Dimensional Representations of Algebras

A polynomial identity for an algebra (or a ring) A A is a polynomial in noncommutative variables that vanishes under any evaluation in A A. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike. The book is divided into four parts. Part 1 contains foundational material on representation theory and noncommutative algebra. In addition to setting the stage for the rest of the book, this part can be used for an introductory course in noncommutative algebra. An expert reader may use Part 1 as reference and start with the main topics in the remaining parts. Part ...

Catalog of Copyright Entries. Third Series
  • Language: en
  • Pages: 1450
Introduction to Orthogonal, Symplectic, and Unitary Representations of Finite Groups
  • Language: en
  • Pages: 305
The Historical Development of Quantum Theory
  • Language: en
  • Pages: 628
Central Simple Algebras and Galois Cohomology
  • Language: en
  • Pages: 431

Central Simple Algebras and Galois Cohomology

The first comprehensive modern introduction to central simple algebra starting from the basics and reaching advanced results.

Quadratic and Hermitian Forms over Rings
  • Language: en
  • Pages: 536

Quadratic and Hermitian Forms over Rings

From its birth (in Babylon?) till 1936 the theory of quadratic forms dealt almost exclusively with forms over the real field, the complex field or the ring of integers. Only as late as 1937 were the foundations of a theory over an arbitrary field laid. This was in a famous paper by Ernst Witt. Still too early, apparently, because it took another 25 years for the ideas of Witt to be pursued, notably by Albrecht Pfister, and expanded into a full branch of algebra. Around 1960 the development of algebraic topology and algebraic K-theory led to the study of quadratic forms over commutative rings and hermitian forms over rings with involutions. Not surprisingly, in this more general setting, alge...