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, JSTOR 1995803, MR 0281839
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