On the deformation of algebra morphisms and diagrams. (English) Zbl 0544.18005

Gerstenhaber, M.; Schack, S. D.

Trans. Am. Math. Soc. 279, 1-50 (1983).

Taking into consideration the similarity between the formal aspects of the deformation theories of complex manifolds and associative algebras, this paper links both of them with a deformation theory for diagrams (a diagram being a functor from a poset to the category of associative algebras) and proves (looking at Yoneda and Hochschild cohmology theories) a cohomology comparison theorem which partially explains the analogy.

Reviewer: G.Hoff

MSC:

18G25	Relative homological algebra, projective classes (category-theoretic aspects)
16S80	Deformations of associative rings
55N35	Other homology theories in algebraic topology
18G10	Resolutions; derived functors (category-theoretic aspects)
32G05	Deformations of complex structures
16E40	(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)

Keywords:

Yoneda cohomology; deformation; diagram; associative algebras; Hochschild cohmology; cohomology comparison theorem

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