arXiv subjects

Yaakov Karasik

Publications and source records attributed to Yaakov Karasik.

2 recordsLinked to original sources

arXiv2015

On the Codimension Sequence of G-Simple Algebras

In the 80's, Regev, using results of Formanek, Procesi and Razmyslov in invariant theory and Hilbert series', determined asymptotically the codimension sequence of mXm matrices over an algebraically closed field of characteristic zero. Inspired by Regev's ideas, we found that the asymptotics of $c_{n}^{G}(A)$, the G graded codimension sequence of a finite dimensional G simple algebra A, is equal to $αn^{\frac{1-\dim(A_{e})}{2}}(\dim(A)^{n} $ (this was conjectured by E.Aljadeff, D.Haile and M. Natapov), where αis not yet determined number. Moreover, in the case where A is the algebra of mXm matrices with an arbitrary elementary G-grading we also manged to calculate α.

math.RA↗

arXiv2015

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

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 $H\otimes\left(F\mathbb{Z}/2\mathbb{Z}\right)^{*}$-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 $f_{1},...,f_{s}$ 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.

math.RA↗