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An introduction to algebraic deformation theory. (English) Zbl 0772.18006
Deformation theory is connected with appropriate cohomology theories by some fundamental results. The author presents the basic definitions and theorems of classical deformation theories. These are unified by triple cohomology. All results appear elsewhere [e.g., M. Gerstenhaber, Ann. Math., II. Ser. 79, 59-103 (1964; Zbl 0123.031), and the author, J. Algebra 105, 437-442 (1987; Zbl 0606.16016)].

MSC:
18C15 Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads
16S80 Deformations of associative rings
16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
13D10 Deformations and infinitesimal methods in commutative ring theory
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