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Article overview
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Kemer's Theory for H-Module Algebras with Application to the PI Exponent | Yaakov Karasik
; | Date: |
1 Sep 2015 | 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
$Hotimesleft(Fmathbb{Z}/2mathbb{Z}
ight)^{*}$-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 $Gamma$ which
contains an ordinary PI contains H-polynomials $f_{1},...,f_{s}$ which
generates $Gamma$ 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. | Source: | arXiv, 1509.0191 | Services: | Forum | Review | PDF | Favorites |
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