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Let F be an algebraically closed field of characteristic zero. In this survey we deal with superalgebras, that is associative algebras graded by the cyclic group of order 2. We present the classification of the so-called pseudoautomorphisms that it is possible to define, up to equivalence, in the full matrix superalgebra \(M_n(F)\) of \(n \times n\) matrices. Moreover, we find the generators of the ideal of identities for the superalgebra \(M_2(F)\) endowed with all possible non-equivalent pseudoautomorphisms.

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On Matrix Superalgebras with Pseudoautomorphism

  • 会议论文

  • 发表日期：

    2025年

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  • Ginevra Giordani,
  • Antonio Ioppolo

摘要

Let F be an algebraically closed field of characteristic zero. In this survey we deal with superalgebras, that is associative algebras graded by the cyclic group of order 2. We present the classification of the so-called pseudoautomorphisms that it is possible to define, up to equivalence, in the full matrix superalgebra \(M_n(F)\) of \(n \times n\) matrices. Moreover, we find the generators of the ideal of identities for the superalgebra \(M_2(F)\) endowed with all possible non-equivalent pseudoautomorphisms.