Let A be a superalgebra over a field F of characteristic zero. We prove tight relations between graded automorphisms, pseudoautomorphisms, superautomorphisms and K-gradings on A, where K is the Klein group. Moreover, we investigate the consequences of such connections within the theory of polynomial identities. In the second part we focus on the superalgebra UTn (F) of n × upper triangular matrices by completely classifying the graded-pseudo-super automorphism that one can define on it. Finally, we compute the ideals of identities of UTn endowed with a graded or a pseudo automorphism, for any n, and the ideals of identities with superautomorphism in the cases n = 2 {n=2} and n = 3 {n=3}.

Gradings and graded linear maps on algebras

Ioppolo A.;
2024-01-01

Abstract

Let A be a superalgebra over a field F of characteristic zero. We prove tight relations between graded automorphisms, pseudoautomorphisms, superautomorphisms and K-gradings on A, where K is the Klein group. Moreover, we investigate the consequences of such connections within the theory of polynomial identities. In the second part we focus on the superalgebra UTn (F) of n × upper triangular matrices by completely classifying the graded-pseudo-super automorphism that one can define on it. Finally, we compute the ideals of identities of UTn endowed with a graded or a pseudo automorphism, for any n, and the ideals of identities with superautomorphism in the cases n = 2 {n=2} and n = 3 {n=3}.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/250500
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