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]/(xⁿ⁺¹) = g⊗_kk[x]/(xⁿ⁺¹) 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 Takiff (1971), who in some cases described the ring of polynomials on these algebras invariant under the action of the adjoint group.

Also Takiff ... groups, superalgebras, supergroups, symmetric spaces, takiffisation of modules.