The term "Weil algebra" is also sometimes used to mean a finite-dimensional real local Artinian ring.

In mathematics, the Weil algebra of a Lie algebra g, introduced by Cartan (1951) based on unpublished work of André Weil, is a differential graded algebra given by the Koszul algebra Λ(g*)⊗S(g*) of its dual g*.

References

• Cartan, Henri (1951), "Notions d'algèbre différentielle; application aux groupes de Lie et aux variétés où opère un groupe de Lie", Colloque de topologie (espaces fibrés), Bruxelles, 1950, Georges Thone, Liège, pp. 15–27, MR 0042426 Reprinted in (Guillemin & Sternberg 1999)
• Guillemin, Victor W.; Sternberg, Shlomo (1999), Supersymmetry and equivariant de Rham theory, Mathematics Past and Present, Berlin, New York: Springer-Verlag, ISBN 978-3-540-64797-3, MR 1689252