Abstract
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 ℤ2 and the algebra of 2 × 2 upper triangular matrices with suitable superautomorphisms.
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The authors were partially supported by GNSAGA of INdAM.
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Ioppolo, A., La Mattina, D. Algebras with superautomorphism: simple algebras and codimension growth. Isr. J. Math. (2024). https://doi.org/10.1007/s11856-024-2663-4
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DOI: https://doi.org/10.1007/s11856-024-2663-4