On the Generalized Enveloping Algebra of a Color Lie Algebra
| dc.creator | Petit, Toukaiddine | |
| dc.creator | Van Oystaeyen, Freddy | |
| dc.date | 2005-12-26 | |
| dc.date.accessioned | 2026-07-07T06:55:46Z | |
| dc.date.available | 2026-07-07T06:55:46Z | |
| dc.description | Let $G$ be an abelien group, $ε$ an anti-bicharacter of $G$ and $L$ a $G$-graded $ε$ Lie algebra (color Lie algebra) over $\K$ a field of characteristic zero. We prove that all $G$-graded, positive filtered $A$ such that the associated graded algebra is isomorphic to the $G$-graded $ε$-symmetric algebra $S(L)$, there is a $G$- graded $ε$-Lie algebra $L$ and a $G$-graded scalar two cocycle $ω\in\mathrm{Z}_{gr}^2(L,\K)$, such that $A$ is isomorphic to $ U_ω(L)$ the generalized enveloping algebra of $L$ associated with $ω$. We also prove there is an isomorphism of graded spaces between the Hochschild cohomology of the generalized universal enveloping algebra $U(L)$ and the generalized cohomology of color Lie algebra $L$. | |
| dc.description | 11 pages, 3 figures, to appear in Algebras and Representation Theory | |
| dc.identifier | https://arxiv.org/abs/math/0512574 | |
| dc.identifier | http://arxiv.org/abs/math/0512574 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106387 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16E40, 17B35, 17B75 | |
| dc.title | On the Generalized Enveloping Algebra of a Color Lie Algebra | |
| dc.type | text |