Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3233
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
First Page
1809
Last Page
1813
Recommended Citation
FINDIK, ŞEHMUS
(2022)
"Symmetric polynomials in the free metabelian associative algebra of rank 2,"
Turkish Journal of Mathematics: Vol. 46:
No.
5, Article 12.
https://doi.org/10.55730/1300-0098.3233
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss5/12
