The purpose of this thesis is to present in the setting of superalgebras with superinvolution some of the most interesting and challenging problems of combinatorial PI-theory (the theory of polynomial identities), which have already been addressed in the field of associative algebras or of algebras with involution. More precisely, I shall characterize the varieties of superalgebras with superinvolution of polynomial growth and along the way I shall classify the subvarieties of the varieties of almost polynomial growth. Finally I shall find standard identities of minimal degree in the setting of matrix superalgebras with superinvolution and in this way I shall show that the Amitsur-Levitzki theorem can be improved by considering only certain kinds of matrices.

Superalgebras with superinvolution / Ioppolo, Antonio. - (2017 Jan 24).

Superalgebras with superinvolution

IOPPOLO, ANTONIO
2017-01-24

Abstract

The purpose of this thesis is to present in the setting of superalgebras with superinvolution some of the most interesting and challenging problems of combinatorial PI-theory (the theory of polynomial identities), which have already been addressed in the field of associative algebras or of algebras with involution. More precisely, I shall characterize the varieties of superalgebras with superinvolution of polynomial growth and along the way I shall classify the subvarieties of the varieties of almost polynomial growth. Finally I shall find standard identities of minimal degree in the setting of matrix superalgebras with superinvolution and in this way I shall show that the Amitsur-Levitzki theorem can be improved by considering only certain kinds of matrices.
24-gen-2017
polynomial identities, superinvolutions, growth, standard polynomials
Superalgebras with superinvolution / Ioppolo, Antonio. - (2017 Jan 24).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/582729
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