In this paper we consider the natural action of a bialgebra H on the algebra UT2(W) corresponding to a given simple H-module W. We prove that these algebras generate varieties with almost polynomial growth of H-codimensions. This generalizes the known results concerning graded algebras and algebras with derivations. In this context, we introduce the space of Y-proper polynomials and we study the sequence of the corresponding cocharacters, which is of independent interest.
H-cocharacters and a class of H-algebras with almost polynomial growth
Argenti, Sebastiano
;Di Vincenzo, Onofrio Mario
2025-01-01
Abstract
In this paper we consider the natural action of a bialgebra H on the algebra UT2(W) corresponding to a given simple H-module W. We prove that these algebras generate varieties with almost polynomial growth of H-codimensions. This generalizes the known results concerning graded algebras and algebras with derivations. In this context, we introduce the space of Y-proper polynomials and we study the sequence of the corresponding cocharacters, which is of independent interest.File in questo prodotto:
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