Let F be an infinite field of characteristic different from 2. We study the ∗-polynomial identities of the ∗-minimal algebra R = UT∗(F ⊕ F, F). We describe the generators of the *-polynomial identities of R and a linear basis of the relatively free algebra of R. When char.F = 0, these results allow us to provide a complete list of polynomials generating irreducible GL × GL-modules decomposing the proper part of the relatively free algebra of R. Finally, the ∗-codimension sequence of R is explicitly computed.
*-Polynomial Identities of a Nonsymmetric *-Minimal Algebra
NARDOZZA, VINCENZO
2014-01-01
Abstract
Let F be an infinite field of characteristic different from 2. We study the ∗-polynomial identities of the ∗-minimal algebra R = UT∗(F ⊕ F, F). We describe the generators of the *-polynomial identities of R and a linear basis of the relatively free algebra of R. When char.F = 0, these results allow us to provide a complete list of polynomials generating irreducible GL × GL-modules decomposing the proper part of the relatively free algebra of R. Finally, the ∗-codimension sequence of R is explicitly computed.File in questo prodotto:
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