{"title":"Algebras with superautomorphism: simple algebras and codimension growth","authors":"Antonio Ioppolo, Daniela La Mattina","doi":"10.1007/s11856-024-2663-4","DOIUrl":null,"url":null,"abstract":"<p>Let <i>A</i> be an associative algebra endowed with a superautomorphism <i>φ</i>. 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 <i>φ</i>-codimensions of <i>A</i> is polynomially bounded if and only if the variety generated by <i>A</i> does not contain the group algebra of ℤ<sub>2</sub> and the algebra of 2 × 2 upper triangular matrices with suitable superautomorphisms.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":"6 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Israel Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11856-024-2663-4","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.
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