TY - JOUR

T1 - Supersymmetric Elements in Divided Powers Algebras

AU - Marko, František

N1 - Publisher Copyright:
© 2020, Springer Nature B.V.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/12/1

Y1 - 2020/12/1

N2 - 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.

AB - 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.

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U2 - 10.1007/s10468-019-09933-0

DO - 10.1007/s10468-019-09933-0

M3 - Article

AN - SCOPUS:85077583007

VL - 23

SP - 2349

EP - 2372

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

SN - 1386-923X

IS - 6

ER -