Let G be a finite group and A a G-graded algebra over a field F of characteristic zero. We characterize the (Formula presented.)-ideals (Formula presented.) of graded identities of A such that the multiplicities (Formula presented.) in the graded cocharacter of A are bounded by one. We do so by exhibiting a set of identities of the (Formula presented.)-ideal. As a consequence we characterize the varieties of G-graded algebras whose lattice of subvarieties is distributive.
Giambruno, A., Polcino Milies, C., Valenti, A. (2018). Cocharacters of group graded algebras and multiplicities bounded by one. LINEAR & MULTILINEAR ALGEBRA, 66(8), 1709-1715 [10.1080/03081087.2017.1369493].
Cocharacters of group graded algebras and multiplicities bounded by one
GIAMBRUNO, Antonino;VALENTI, Angela
2018-01-01
Abstract
Let G be a finite group and A a G-graded algebra over a field F of characteristic zero. We characterize the (Formula presented.)-ideals (Formula presented.) of graded identities of A such that the multiplicities (Formula presented.) in the graded cocharacter of A are bounded by one. We do so by exhibiting a set of identities of the (Formula presented.)-ideal. As a consequence we characterize the varieties of G-graded algebras whose lattice of subvarieties is distributive.
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