Rings with Polynomial Identities and Finite Dimensional Representations of Algebras

ISBN-13: 9781470451745 / Miękka / 2020 / 630 str.

Amitai Regev

Spis treści

• Introduction
• Foundations: Noncommutative algebra
• Universal algebra
• Symmetric functions and matrix invariants
• Polynomial maps
• Azumaya algebras and irreducible representations
• Tensor symmetry
• Combinatorial aspects of polynomial identities: Growth
• Shirshov's theorem
• $2\times2$ matrices
• The structure theorems
• Matrix identities
• Structure theorems
• Invariants and trace identities
• Involutions and matrices
• A geometric approach
• Spectrum and dimension
• The relatively free algebras: The nilpotent radical
• Finite-dimensional and affine PI algebras
• The relatively free algebras
• Identities and superalgebras
• The Specht problem
• The PI-exponent
• Codimension growth for matrices
• Codimension growth for algebras satisfying a Capelli identity
• The Golod-Shafarevich counterexamples
• Bibliography
• Index
• Index of Symbols.