具有超同构性的代数：简单代数与维数增长

IF 0.8 2区数学 Q2 MATHEMATICS

Israel Journal of Mathematics Pub Date : 2024-09-03 DOI:10.1007/s11856-024-2663-4

Antonio Ioppolo, Daniela La Mattina

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引用次数: 0

摘要

让 A 是一个具有超同构 φ 的关联代数。在本文中，我们完整地分类了具有阶数≤ 2 的超同构的有限维简单代数。此外，在此背景下推广韦德本-马尔切夫定理后，我们证明了当且仅当由 A 生成的综不包含ℤ2 的群代数和具有适当超同构的 2 × 2 上三角矩阵代数时，A 的 φ 多维数序列是多项式有界的。

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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-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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来源期刊

Israel Journal of Mathematics 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

审稿时长

6 months

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.