Computational aspects of polynomial identities Volume l Kemer s Theorems Kanel-Belov

This completed downloadable of Computational aspects of polynomial identities Volume l Kemer s Theorems Kanel-Belov

Instant downloaded Computational aspects of polynomial identities Volume l Kemer s Theorems Kanel-Belov pdf docx epub after payment.

Product details:

• ISBN-10 ‏ : ‎ 9781498720083
• ISBN-13 ‏ : ‎ 978-1498720083
• Author:  Alexei Kanel-Belov (Author), Yakov Karasik (Author), Louis Halle Rowen (Author)

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:

Part I: Basic Associative PI-Theory

Chapter 1: Basic Results

Chapter 2: A Few Words Concerning Affine PI-Algebras: Shirshov’s Theorem

Chapter 3: Representations of Sn and Their Applications

Part II: Affine PI-Algebras

Chapter 4: The Braun-Kemer-Razmyslov Theorem

Chapter 5: Kemer’s Capelli Theorem

Part III: Specht’s Conjecture

Chapter 6: Specht’s Problem and Its Solution in the Affine Case (Characteristic 0)

Chapter 7: Superidentities and Kemer’s Solution for Non-Affine Algebras

Chapter 8: Trace Identities

Chapter 9: PI-Counterexamples in Characteristic p

Chapter 10: Recent Structural Results

Chapter 11: Poincare-Hilbert Series and Gel’fand-Kirillov Dimension

Chapter 12: More Representation Theory

Part IV: Supplementary Material

People also search:

thermodynamic models fundamentals & computational aspects

computational aspects of robotics

genomics and proteomics functional and computational aspects

recursion theory computational aspects of definability

computational aspects of cooperative game theory pdf