Kemer's Theory for H-Module Algebras with Application to the PI Exponent

2015/09/01 by Karasik, Yaakov · 1 citation
#16R10 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1509.00191

Abstract

Let H be a semisimple finite dimensional Hopf algebra over a field F of zero characteristic. We prove three major theorems: 1. The Representability theorem which states that every H-module (associative) F-algebra W satisfying an ordinary PI, has the same H-identities as the Grassmann envelope of an H⊗(Fℤ/2ℤ)^*-module algebra which is finite dimensional over a field extension of F. 2. The Specht problem for H-module (ordinary) PI algebras. That is, every H-T-ideal Γ which contains an ordinary PI contains H-polynomials f₁,...,f_s which generates Γ as an H-T-ideal. 3. Amitsur's conjecture for H-module algebras, saying that the exponent of the H-codimension sequence of an ordinary PI H-module algebra is an integer.

Cited by

• Cocharacters of generalized polynomial identities

Related

• One proof of the original Kemer's theorems (concerning the text of C. Procesi "What happened to PI-theory", arxiv.org/abs/1403.5673)
• Partial Hopf-Galois theory
• Hopf algebras of dimension 14
• Partial Representations of Hopf Algebras
• Semisimple Hopf algebras of dimension pq are trivial