dorsal/arxiv
View SchemaCohomology of Drinfel'd algebras: A General Nonsense Approach
| Authors | Martin Markl, Steve Shnider |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9505002 |
| URL | https://arxiv.org/abs/q-alg/9505002 |
Abstract
In our paper [Markl, Shnider: Drinfel'd Algebra Deformations and the Associahedra, IMRN 1994, no. 4, 169-176] we announced a construction of a cohomology controlling deformations of quasi-coassociative (or Drinfel'd) bialgebras. The full version of the paper will appear as [Markl, Shnider: Drinfel'd Algebra Deformations, Homotopy Comodules and the Associahedra] in Trans. Amer. Math. Soc. The construction in the paper was based on very explicit arguments using deep combinatorial properties of the associahedra. The present paper gives an alternative, general nonsense approach to the construction. So, we just prove the existence of such a cohomology without explicitly constructing it. This should be compared with the two approaches to the cohomology of associative algebras: we either describe explicitly the Hochschild complex and say "Behold! this is the cohomology" or we prove the existence of a projective resolution and define the cohomology as the derived functor.
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"abstract": "In our paper [Markl, Shnider: Drinfel\u0027d Algebra Deformations and the\nAssociahedra, IMRN 1994, no. 4, 169-176] we announced a construction of a\ncohomology controlling deformations of quasi-coassociative (or Drinfel\u0027d)\nbialgebras. The full version of the paper will appear as [Markl, Shnider:\nDrinfel\u0027d Algebra Deformations, Homotopy Comodules and the Associahedra] in\nTrans. Amer. Math. Soc. The construction in the paper was based on very\nexplicit arguments using deep combinatorial properties of the associahedra. The\npresent paper gives an alternative, general nonsense approach to the\nconstruction. So, we just prove the existence of such a cohomology without\nexplicitly constructing it. This should be compared with the two approaches to\nthe cohomology of associative algebras: we either describe explicitly the\nHochschild complex and say \"Behold! this is the cohomology\" or we prove the\nexistence of a projective resolution and define the cohomology as the derived\nfunctor.",
"arxiv_id": "q-alg/9505002",
"authors": [
"Martin Markl",
"Steve Shnider"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Cohomology of Drinfel\u0027d algebras: A General Nonsense Approach",
"url": "https://arxiv.org/abs/q-alg/9505002"
},
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