Filtering bases and cohomology of nilpotent subalgebras of Witt and $\widetilde{sl}_2$ Lie algebras
| dc.creator | Weinstein, F. V. | |
| dc.date | 2006-04-28 | |
| dc.date | 2006-05-05 | |
| dc.date.accessioned | 2026-07-07T07:11:22Z | |
| dc.date.available | 2026-07-07T07:11:22Z | |
| dc.description | We study the cohomology with trivial coefficients of Lie algebras L_k of the polynomial vector fields on the line with zero $k$-jet, (k>=1), and the cohomology of the similar subalgebras {L}_k of the polynomial loops algebra $\widetilde{sl}_2$. In both cases we construct the special bases (filtering bases) in the external complexes of these algebras. A spectral sequence based on this construction allows to completely find the cohomology of L_k and {L}_k. We also apply the filtering bases to find the spectral resolution of the Laplace operators for algebras L_1 and L_0, and obtain explicit formulas for the representing cycles of homologies for algebras L_k and {L}_k by means of the Schur polynomials. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0604631 | |
| dc.identifier | http://arxiv.org/abs/math/0604631 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111729 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 17B68 | |
| dc.title | Filtering bases and cohomology of nilpotent subalgebras of Witt and $\widetilde{sl}_2$ Lie algebras | |
| dc.type | text |