Gradings and graded linear maps on algebras-Reference-Cited by-同舟云学术

Gradings and graded linear maps on algebras

Published:2024-08-05 Issue: Volume: Page:
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Ioppolo Antonio¹,Martino Fabrizio²

Affiliation:

1. Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica , Università degli Studi dell’Aquila , Via Vetoio 1, 67100 , L’Aquila , Italy

2. Dipartimento di Matematica e Informatica , 18998 Università degli Studi di Palermo , Via Archirafi 34, 90123 , Palermo , Italy

Abstract

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 U ⁢ T n ⁢ ( F )

{UT_{n}(F)}

of n × n

{n\times 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 U ⁢ T n ⁢ ( F )

{UT_{n}(F)}

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}

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/forum-2024-0098/pdf

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