On the cohomology of vector fields on parallelizable manifolds
| dc.creator | Billig, Yuly | |
| dc.creator | Neeb, Karl-Hermann | |
| dc.date | 2007-05-23 | |
| dc.date.accessioned | 2026-07-07T08:02:59Z | |
| dc.date.available | 2026-07-07T08:02:59Z | |
| dc.description | In the present paper we determine for each parallelizable smooth compact manifold $M$ the cohomology spaces $H^2(V_M,\barΩ^p_M)$ of the Lie algebra $V_M$ of smooth vector fields on $M$ with values in the module $\barΩ^p_M = Ω^p_M/dΩ^{p-1}_M$. The case of $p=1$ is of particular interest since the gauge algebra $C^\infty (M,k)$ has the universal central extension with center $\barΩ^1_M$, generalizing affine Kac-Moody algebras. The second cohomology $H^2(V_M, \barΩ^1_M)$ classifies twists of the semidirect product of $V_M$ with the universal central extension $C^\infty (M,k) \oplus \barΩ^1_M$. | |
| dc.identifier | https://arxiv.org/abs/0705.3382 | |
| dc.identifier | http://arxiv.org/abs/0705.3382 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129417 | |
| dc.subject | Representation Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 17B56; 17B65; 17B68 | |
| dc.title | On the cohomology of vector fields on parallelizable manifolds | |
| dc.type | text |