Semiinfinite cohomology of associative algebras and bar duality
| dc.creator | Arkhipov, Sergey | |
| dc.date | 1996-02-05 | |
| dc.date.accessioned | 2026-07-07T09:16:49Z | |
| dc.date.available | 2026-07-07T09:16:49Z | |
| dc.description | We describe semiinfinite cohomology of associative algebras in terms of Koszul (or bar) duality. Consider an associative algebra $A$ and two its subalgebras $B$ and $N$ such that $A=B\otimes N$ as a vector space. We prove that the endomorphism algebra of the semiregular $A$-module appears naturally in semiinfinite cohomology theory as a ``two times Koszul dual'' to the algebra $A$. We compare semiinfinite cohomology of universal enveloping algebras with the well-known Lie algebra semiinfinite cohomology. A new description of the critical 2-cocycle is provided. As a consequence we obtain another proof of the fact that additive categories generated by Verma modules over affine Lie algebras on dual levels are antiequivalent. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/q-alg/9602013 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9602013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153492 | |
| dc.subject | Quantum Algebra | |
| dc.title | Semiinfinite cohomology of associative algebras and bar duality | |
| dc.type | text |