Description
Book SynopsisComputational Aspects of Polynomial Identities: Volume l, Kemer's Theorems, 2nd Edition presents the underlying ideas in recent polynomial identity (PI)-theory and demonstrates the validity of the proofs of PI-theorems. This edition gives all the details involved in Kemer's proof of Specht's conjecture for affine PI-algebras in characteristic 0.
The book first discusses the theory needed for Kemer's proof, including the featured role of Grassmann algebra and the translation to superalgebras. The authors develop Kemer polynomials for arbitrary varieties as tools for proving diverse theorems. They also lay the groundwork for analogous theorems that have recently been proved for Lie algebras and alternative algebras. They then describe counterexamples to Specht's conjecture in characteristic p as well as the underlying theory. The book also covers Noetherian PI-algebras, PoincaréHilbert series, GelfandKirillov dimension, the comb
Table of Contents
Basic Associative PI-Theory: Basic Results. A Few Words Concerning Affine PI-Algebras: Shirshov’s Theorem. Representations of Sn and Their Applications. Affine PI-Algebras: The Braun-Kemer-Razmyslov Theorem. Kemer’s Capelli Theorem. Specht’s Conjecture: Specht’s Problem and Its Solution in the Affine Case (Characteristic 0). Superidentities and Kemer’s Solution for Non-Affine Algebras. Trace Identities. PI-Counterexamples in Characteristic p. Other Results for Associative PI-Algebras: Recent Structural Results. Poincaré-Hilbert Series and Gelfand-Kirillov Dimension. More Representation Theory. Supplementary Material: List of Theorems. Some Open Questions. Bibliography.
