Computational aspects of polynomial identities. Kemer's theorems / Volume I, (2015)

• Record Type: Book
• Other Titles: Kemer's theorems
• Further Information: Note: Alexei Kanel-Belov, Yakov Karasik, Louis Halle Rowen.
• Authors: Kanel-Belov, Alexei, 1963-; Karasik, Yakov; Rowen, Louis Halle
• Contents: Basic Associative PI-Theory; Basic Results; Preliminary Definitions; Noncommutative Polynomials and Identities; Graded Algebras; Identities and Central Polynomials of Matrices ; Review of Major Structure Theorems in PI Theory; Representable Algebras; Sets of Identities; Relatively Free Algebras; Generalized Identities A Few Words Concerning Affine PI-Algebras: Shirshov’s Theorem; Words Applied to Affine Algebras; Shirshov’s Height Theorem; Shirshov’s Lemma; The Shirshov Program; The Trace Ring; Shirshov’s Lemma Revisited; Appendix A: The Independence Theorem for Hyperwords; Appendix B: A Subexponential Bound for the Shirshov Height Representations of Sn and Their Applications; Permutations and identities; Review of the Representation Theory of Sn ; Sn -Actions on Tn (V ); Codimensions and Regev’s Theorem; Multilinearization Affine PI-Algebras; The Braun-Kemer-Razmyslov Theorem; Structure of the Proof; A Cayley-Hamilton Type Theorem; The Module M over the Relatively Free Algebra C{X, Y, Z} of cn +1; The Obstruction to Integrality Obstn (A ) ⊆ A ; Reduction to Finite Modules; Proving that Obstn (A ) · (CAPn (A ))2 = 0; The Shirshov Closure and Shirshov Closed Ideals Kemer’s Capelli Theorem; First Proof (Combinatoric); Second Proof (Pumping plus Representation Theory) Specht’s Conjecture; Specht’s Problem and Its Solution in the Affine Case (Characteristic 0); Specht’s Problem Posed; Early Results on Specht’s Problem; Kemer’s PI-Representability Theorem; Multiplying Alternating Polynomials, and the First Kemer Invariant; Kemer’s First Lemma; Kemer’s Second Lemma; Significance of Kemer’s First and Second Lemmas; Manufacturing Representable Algebras; Kemer’s PI-Representability Theorem Concluded; Specht’s Problem Solved for Affine Algebras; Pumping Kemer Polynomials; Appendix: Strong Identities and Specht’s Conjecture Superidentities and Kemer’s Solution for Non-Affine Algebras; Superidentities; Kemer’s Super-PI Representability Theorem; Kemer’s Main Theorem Concluded; Consequences of Kemer’s Theory Trace Identities; Trace Polynomials and Identities; Finite Generation of Trace T -Ideals; Trace Codimensions; Kemer’s Matrix Identity Theorem in Characteristic p PI-Counterexamples in Characteristic p ; De-Multilinearization; The Extended Grassmann Algebra; Non-Finitely Based T -Ideals in Characteristic ; Non-Finitely Based T -Ideals in Odd Characteristic Other Results for Associative PI-Algebras; Recent Structural Results; Left Noetherian PI-Algebras; Identities of Group Algebras; Identities of Enveloping Algebras Poincaré-Hilbert Series and Gelfand-Kirillov Dimension; The Hilbert Series of an Algebra; The Gelfand-Kirillov Dimension; Rationality of Certain Hilbert Series; The Multivariate Poincaré-Hilbert Series More Representation Theory; Cocharacters; GL (V )-Representation Theory Supplementary Material; List of Theorems Some Open Questions Bibliography
• Edition: Second edition
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2015
• Extent: 1 online resource
• Subjects: 512.9; Polynomials; PI-algebras
• Languages: English
• ISBNs: 9781498720090
• Related ISBNs: 9781498720083
• Notes: Note: Description based on CIP data; item not viewed.
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