Symmetric polynomials in the free metabelian associative algebra of rank 2

Authors: ŞEHMUS FINDIK

Abstract: Let $F$ be the free metabelian associative algebra generated by $x$ and $y$ over a field of characteristic zero. We call a polynomial $f\in F$ symmetric, if $f(x,y)=f(y,x)$. The set of all symmetric polynomials coincides with the algebra $F^{S_2}$ of invariants of the symmetric group $S_2$. In this paper, we give the full description of the algebra $F^{S_2}$.

Keywords: Metabelian, symmetric polynomial

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