Turkish Journal of Mathematics
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 $F^{S_2}$.
DOI
10.55730/1300-0098.3233
Keywords
Metabelian, symmetric polynomial
First Page
1809
Last Page
1813
Recommended Citation
FINDIK, Ş (2022). Symmetric polynomials in the free metabelian associative algebra of rank 2. Turkish Journal of Mathematics 46 (5): 1809-1813. https://doi.org/10.55730/1300-0098.3233
