On the symmetric polynomials in the variety of Grassmann algebras

Abstract

Let 𝐾 be a field of characteristic zero and 𝐿 be the associative algebra of rank 2 over 𝐾 in the variety generated by Grassmann algebras. In this paper, we study the subalgebra 𝐿 𝑆 2 of symmetric polynomials in the algebra 𝐿, and give a finite generating set for 𝐿 𝑆 2 .