Supersymmetric Elements in Divided Powers Algebras

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Abstract

Description of adjoint invariants of general linear Lie superalgebras gl(m| n) by Kantor and Trishin was given in terms of supersymmetric polynomials. Later, generators of invariants of the adjoint action of the general linear supergroup GL(m|n) and generators of supersymmetric polynomials were determined over fields of positive characteristic. In this paper, we introduce the concept of supersymmetric elements in the divided powers algebra Div[x1,…, xm, y1,…, yn], and give a characterization of supersymmetric elements via a system of linear equations. Then we determine generators of supersymmetric elements for divided powers algebras in the cases when n = 0, n = 1, and m ≤ 2, n = 2.

Original languageEnglish (US)
Pages (from-to)2349-2372
Number of pages24
JournalAlgebras and Representation Theory
Volume23
Issue number6
DOIs
StatePublished - Dec 1 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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