0000000001052456
AUTHOR
Irina Sviridova
Asymptotics for the multiplicities in the cocharacters of some PI-algebras
We consider associative PI-algebras over a field of characteristic zero. We study the asymptotic behavior of the sequence of multiplicities of the cocharacters for some significant classes of algebras. We also give a characterization of finitely generated algebras for which this behavior is linear or quadratic.
Identities of PI-Algebras Graded by a Finite Abelian Group
We consider associative PI-algebras over an algebraically closed field of zero characteristic graded by a finite abelian group G. It is proved that in this case the ideal of graded identities of a G-graded finitely generated PI-algebra coincides with the ideal of graded identities of some finite dimensional G-graded algebra. This implies that the ideal of G-graded identities of any (not necessary finitely generated) G-graded PI-algebra coincides with the ideal of G-graded identities of the Grassmann envelope of a finite dimensional (G × ℤ2)-graded algebra, and is finitely generated as GT-ideal. Similar results take place for ideals of identities with automorphisms.
Asymptotics for multiplicities in the cocharacters of some PI-algebras
We consider associative PI-algebras over a eld of characteristic zero. We study the asymptotic behavior of the sequence of multiplicities of the cocharacters for some signi cant classes of algebras. We also give a characterization of nitely generated algebras for which this behavior is linear or quadratic.
Asymptotics for the Amitsur's Capelli - Type Polynomials and Verbally Prime PI-Algebras
We consider associativePI-algebras over a field of characteristic zero. The main goal of the paper is to prove that the codimensions of a verbally prime algebra [11] are asymptotically equal to the codimensions of theT-ideal generated by some Amitsur's Capelli-type polynomialsEM,L* [1]. We recall that two sequencesan,bnare asymptotically equal, and we writean≃bn,if and only if limn→∞(an/bn)=1.In this paper we prove that\(c_n \left( {M_k \left( G \right)} \right) \simeq c_n \left( {E_{k^2 ,k^2 }^ * } \right) and c_n \left( {M_{k,l} \left( G \right)} \right) \simeq c_n \left( {E_{k^2 + l^2 ,2kl}^ * } \right) \)% MathType!End!2!1!, whereG is the Grassmann algebra. These results extend to all v…