We study the growth of the codimensions of a *-superalgebra over a field of characteristic zero. We classify the ideals of identities of finite dimensional algebras whose corresponding codimensions are of almost polynomial growth. It turns out that these are the ideals of identities of two algebras with distinct involutions and gradings. Along the way, we also classify the finite dimensional simple *-superalgebras over an algebraically closed field of characteristic zero.
Giambruno, A., dos Santos, R., Vieira, A. (2016). Identities of *-superalgebras and almost polynomial growth. LINEAR & MULTILINEAR ALGEBRA, 64(3), 484-501 [10.1080/03081087.2015.1049933].
Identities of *-superalgebras and almost polynomial growth
GIAMBRUNO, Antonino;
2016-01-01
Abstract
We study the growth of the codimensions of a *-superalgebra over a field of characteristic zero. We classify the ideals of identities of finite dimensional algebras whose corresponding codimensions are of almost polynomial growth. It turns out that these are the ideals of identities of two algebras with distinct involutions and gradings. Along the way, we also classify the finite dimensional simple *-superalgebras over an algebraically closed field of characteristic zero.
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