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- W4285772094 abstract "Let $K[X_n]$ be the commutative polynomial algebra in the variables $X_n={x_1,ldots,x_n}$ over a field $K$ of characteristic zero. A theorem from undergraduate course of algebra states that the algebra $K[X_n]^{S_n}$ of symmetric polynomials is generated by the elementary symmetric polynomials which are algebraically independent over $K$. In the present paper we study a noncommutative and nonassociative analogue of the algebra $K[X_n]^{S_n}$ replacing $K[X_n]$ with the free metabelian Lie algebra $F_n$ of rank $ngeq 2$ over $K$. It is known that the algebra $F_n^{S_n}$ is not finitely generated but its ideal $(F_n')^{S_n}$ consisting of the elements of $F_n^{S_n}$ in the commutator ideal $F_n'$ of $F_n$ is a finitely generated $K[X_n]^{S_n}$-module. In our main result we describe the generators of the $K[X_n]^{S_n}$-module $(F_n')^{S_n}$ which gives the complete description of the algebra $F_n^{S_n}$." @default.
- W4285772094 created "2022-07-19" @default.
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- W4285772094 date "2019-12-02" @default.
- W4285772094 modified "2023-10-17" @default.
- W4285772094 title "Symmetric polynomials in the free metabelian Lie algebras" @default.
- W4285772094 doi "https://doi.org/10.48550/arxiv.1912.01066" @default.
- W4285772094 hasPublicationYear "2019" @default.
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