Let F be a finitely generated free algebra in a variety of algebras over a field of characteristic zero. A polynomial in F is called symmetric, if it is preserved under any permutation of the generators. The set S(F) of symmetric polynomials is a subalgebra of F. In this talk, we examine the algebras S(F), where F is the free metabelian associative, Lie, Leibniz, Poisson algebra or the free algebra generated by generic traceless matrices or the free algebra in the variety generated by Grassmann algebras.
This video is part of the European Non-Associative Algebra Seminar series.
