Algebraic deformations and triple cohomology. (English) Zbl 0457.16016
MSC:
16S80 | Deformations of associative rings |
16B50 | Category-theoretic methods and results in associative algebras (except as in 16D90) |
17B56 | Cohomology of Lie (super)algebras |
13D10 | Deformations and infinitesimal methods in commutative ring theory |
18D20 | Enriched categories (over closed or monoidal categories) |
18C15 | Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads |
Keywords:
triples; enrichment of category of coalgebras; Barr-Beck cohomology groups; enriched cohomology groups; cohomology of deformed algebrasReferences:
[1] | Michael Barr, Coalgebras over a commutative ring, J. Algebra 32 (1974), no. 3, 600 – 610. · Zbl 0305.18006 · doi:10.1016/0021-8693(74)90161-6 |
[2] | Michael Barr and Jon Beck, Homology and standard constructions, Sem. on Triples and Categorical Homology Theory (ETH, Zürich, 1966/67), Springer, Berlin, 1969, pp. 245 – 335. · Zbl 0176.29003 |
[3] | J. Beck, Triples, algebras and cohomology, Dissertation, Columbia University (1967). |
[4] | Jane Purcell Coffee, Filtered and associated graded rings, Bull. Amer. Math. Soc. 78 (1972), 584 – 587. · Zbl 0262.16028 |
[5] | T. F. Fox, Universal coalgebras, Dissertation, McGill University (1977). |
[6] | Murray Gerstenhaber, On the deformation of rings and algebras, Ann. of Math. (2) 79 (1964), 59 – 103. · Zbl 0123.03101 · doi:10.2307/1970484 |
[7] | Murray Gerstenhaber, On the deformation of rings and algebras. II, Ann. of Math. 84 (1966), 1 – 19. · Zbl 0147.28903 · doi:10.2307/1970528 |
[8] | Murray Gerstenhaber, On the deformation of rings and algebras. IV, Ann. of Math. (2) 99 (1974), 257 – 276. · Zbl 0281.16016 · doi:10.2307/1970900 |
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