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
drensky@math.bas.bg
Sehmus Findik
Dept. of Mathematics, Cukurova University, 01330 Balcali - Adana, Turkey
sfindik@cu.edu.tr
[Abstract-pdf]
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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