Semi-Direct Products Involving Sp 2 n or Spin n with Free Algebras of Symmetric Invariants

Abstract

This is a part of an ongoing project, the goal of which is to classify all semi-direct products \\({\\mathfrak {s}}={\\mathfrak g}{\\ltimes }V\\) such that \\({\\mathfrak g}\\) is a simple Lie algebra, V is a \\({\\mathfrak g}\\)-module, and \\({\\mathfrak {s}}\\) has a free algebra of symmetric invariants. In this paper, we obtain such a classification for the representations of the orthogonal and symplectic algebras.