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Journal of Lie Theory 29 (2019), No. 4, 1071--1092
Copyright Heldermann Verlag 2019

Classical Invariant Theory for Free Metabelian Lie Algebras

Vesselin Drensky
Inst. of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria

Sehmus Findik
Dept. of Mathematics, Cukurova University, 01330 Balcali - Adana, Turkey


Let $W_d=K^d$ be the $d$-dimensional vector space over a field $K$ of characteristic 0 with the canonical action of the general linear group $GL_d(K)$ and let $KX_d$ be the vector space of the linear functions on $W_d$. One of the main topics of classical invariant theory is the study of the algebra of invariants $K[X_d]^{SL_2(K)}$ of the special linear group $SL_2(K)$, when $KX_d$ is a direct sum of $SL_2(K)$-modules of binary forms. Noncommutative invariant theory deals with the algebra of invariants $F_d({\mathfrak V})^G$ of a group $G
Keywords: Free metabelian Lie algebras, classical invariant theory, noncommutative invariant theory.

MSC: 17B01, 17B30, 13A50, 15A72, 17B63.

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