Let A be a finite-dimensional superalgebra with superautomorphism phi over a field of characteristic zero. In [11] the authors gave a positive answer to the Amitsur's conjecture in this setting showing that the phi-exponent of A exists and it is an integer. In the present paper we extend the notion of minimal variety to the context of superalgebras with superautomorphism and prove that a variety is minimal of fixed phi-exponent if, and only if, it is generated by a subalgebra of an upper block triangular matrix algebra equipped with a suitable elementary Z 2-grading and superautomorphism. Along the way, we give a contribution on the isomorphism question within the theory of polynomial identities. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
On minimal varieties of superalgebras with superautomorphism
Ioppolo A.;
2024-01-01
Abstract
Let A be a finite-dimensional superalgebra with superautomorphism phi over a field of characteristic zero. In [11] the authors gave a positive answer to the Amitsur's conjecture in this setting showing that the phi-exponent of A exists and it is an integer. In the present paper we extend the notion of minimal variety to the context of superalgebras with superautomorphism and prove that a variety is minimal of fixed phi-exponent if, and only if, it is generated by a subalgebra of an upper block triangular matrix algebra equipped with a suitable elementary Z 2-grading and superautomorphism. Along the way, we give a contribution on the isomorphism question within the theory of polynomial identities. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.