Eli Aljadeff
Simple G-graded algebras and their polynomial identities.
Tue, 07/26/2011 - 15:01 — SomNambulAuthors: Eli Aljadeff, Darrell Haile
Subjects: Rings and Algebras
AbstractLet G be any group and F an algebraically closed field of characteristic
zero. We show that any two G-graded finite dimensional G-simple algebras over F
are G-graded isomorphic if and only if the satisfy the same G-graded polynomial
identities. This result was proved by Koshlukov and Zaicev in case G is
abelian.Group graded PI-algebras and their codimension growth.
Tue, 02/09/2010 - 16:01 — SomNambulAuthors: Eli Aljadeff
Subjects: Rings and Algebras
AbstractLet W be an associative PI-algebra over a field F of characteristic zero.
Suppose W is G-graded where G is a finite group. Let exp(W) and exp(W_e) denote
the codimension growth of W and of the identity component W_e, respectively.
The following inequality had been conjectured by Bahturin and Zaicev:
exp(W)\leq |G|^2 exp(W_e). The inequality is known in case the algebra W is
affine (i.e. finitely generated). Here we prove the conjecture in general.On the codimension growth of G-graded algebras.
Tue, 08/18/2009 - 11:53 — SomNambulAuthors: Eli Aljadeff
Subjects: Rings and Algebras
AbstractLet W be an associative PI affine algebra over a field F of characteristic
zero. Suppose W is G-graded where G a finite group. Let exp(W) and exp(W_e)
denote the codimension growth of W and W_e respectively. (Here W_e,(e in G)
denotes the identity component of W.) We prove: exp(W) is bounded (from above)
by ord(G)^2 exp(W_{e}). This was conjectured by in Y. A. Bahturin and M. V.
Zaicev, Identities of graded algebras and codimension growth, Trans. Amer.
Math. Soc. {356} (2004), no. 10, 3939--3950.
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