Takiff algebra
In mathematics, a Takiff algebra is a Lie algebra over a truncated polynomial ring. More precisely, a Takiff algebra of a Lie algebra "g" over a field "k" is a Lie algebra of the form "g"["x"]/("x") = "g"⊗"k"["x"]/("x") for some positive integer "n". Sometimes these are called generalized Takiff algebras, and the name "Takiff algebra" is used for the case when "n" = 1. These algebras (for "n" = 1) were studied by , who in some cases described the ring of polynomials on these algebras invariant under the action of the adjoint group.