Algebras with superautomorphism: simple algebras and codimension growth

Let A be an associative algebra endowed with a superautomorphism φ . In this paper we completely classify the finite-dimensional simple algebras with superautomorphism of order ≤ 2. Moreover, after generalizing the Wedderburn–Malcev Theorem in this setting, we prove that the sequence of φ -codimensi...

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Bibliographic Details
Published in:Israel journal of mathematics 2024-09
Main Authors: Ioppolo, Antonio, La Mattina, Daniela
Format: Article
Language:English
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Summary:Let A be an associative algebra endowed with a superautomorphism φ . In this paper we completely classify the finite-dimensional simple algebras with superautomorphism of order ≤ 2. Moreover, after generalizing the Wedderburn–Malcev Theorem in this setting, we prove that the sequence of φ -codimensions of A is polynomially bounded if and only if the variety generated by A does not contain the group algebra of ℤ 2 and the algebra of 2 × 2 upper triangular matrices with suitable superautomorphisms.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-024-2663-4