
Journal of Lie Theory 29 (2019), No. 4, 10711092 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 drensky@math.bas.bg Sehmus Findik Dept. of Mathematics, Cukurova University, 01330 Balcali  Adana, Turkey sfindik@cu.edu.tr [Abstractpdf] 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. [ Fulltextpdf (182 KB)] for subscribers only. 