Description of adjoint invariants of general linear Lie superalgebras \(\mathfrak {gl}(m|n)\) 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,…, x_m, y₁,…, y_n], 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.

Kantor和Trishin用超对称多项式描述了一般线性Lie超代数\（\ mathfrak {gl}（m | n）\）的伴随不变量。后来，在正特性场上确定了一般线性超群G L（m | n）伴随作用的不变量生成器和超对称多项式的生成器。在本文中，我们介绍了除幂代数D i v [ x ₁，…，x _m，y ₁，…，y _n中的超对称元素的概念。]，并通过线性方程组表征超对称元素。然后，我们确定超对称元件的发电机在箱子划分权力代数时Ñ = 0，Ñ = 1，和米≤2，Ñ = 2。