Computational Aspects of Polynomial Identities Volume 1 Kemers Theorems 2nd Edition by Alexei Kanel-Belov, Yakov Karasik, Louis Halle Rowen ISBN 0367445808 978-0367445805

Computational Aspects of Polynomial Identities Volume 1 Kemers Theorems 2nd Edition by Alexei Kanel-Belov, Yakov Karasik,  Louis Halle Rowen- Ebook PDF Instant Download/Delivery: 0367445808, 978-0367445805
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Product details: 

ISBN 10: 0367445808 

ISBN 13: 978-0367445805

Author:  Alexei Kanel-Belov, Yakov Karasik,  Louis Halle Rowen

Computational 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, Poincaré–Hilbert series, Gelfand–Kirillov dimension, the combinatoric theory of affine PI-algebras, and homogeneous identities in terms of the representation theory of the general linear group GL.

Through the theory of Kemer polynomials, this edition shows that the techniques of finite dimensional algebras are available for all affine PI-algebras. It also emphasizes the Grassmann algebra as a recurring theme, including in Rosset’s proof of the Amitsur–Levitzki theorem, a simple example of a finitely based T-ideal, the link between algebras and superalgebras, and a test algebra for counterexamples in characteristic p.

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

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Alexei Kanel-Belov,Yakov Karasik,Louis Halle Rowen,Computational Aspects,Polynomial Identities