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Deformation theory of geometric and algebraic structures. (English) Zbl 0684.58047
Deformation theory of algebras and structures and applications, Nato Adv. Study Inst., Castelvecchio-Pascoli/Italy 1986, Nato ASI Ser., Ser. C 247, 829-838 (1988).
Summary: [For the entire collection see Zbl 0654.00006.]
The purpose of this lecture is to solve the conjecture about the existence of a link between the deformation theory of geometric structures (D. C. Spencer,...) and the deformation theory of algebraic structures (M. Gerstenhaber,...). The original tool, created for this purpose, is called “deformation cohomology” and generalizes, for Lie equations, the Chevalley-Eilenberg cohomology for finite dimensional Lie algebras.
MSC:
58J99 Partial differential equations on manifolds; differential operators
17B56 Cohomology of Lie (super)algebras