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.

References

• Takiff, S. J. (1971), "Rings of invariant polynomials for a class of Lie algebras", Transactions of the American Mathematical Society 160: 249–262, doi:10.2307/1995803, ISSN 0002-9947