Combinatorial bases for multilinear parts of free algebras with double compatible brackets
| dc.creator | Liu, Fu | |
| dc.date | 2008-08-26 | |
| dc.date.accessioned | 2026-07-07T09:58:26Z | |
| dc.date.available | 2026-07-07T09:58:26Z | |
| dc.description | Let X be an ordered alphabet. Lie_2(n) (and P_2(n) respectively) are the multilinear parts of the free Lie algebra (and the free Poisson algebra respectively) on X with a pair of compatible Lie brackets. In this paper, we prove the dimension formulas for these two algebras conjectured by B. Feigin by constructing bases for Lie_2(n) (and P_2(n)) from combinatorial objects. We also define a complementary space Eil_2(n) to Lie_2(n), give a pairing between Lie_2(n) and Eil_2(n), and show that the pairing is perfect. | |
| dc.description | 38 pages; 10 figures | |
| dc.identifier | https://arxiv.org/abs/0808.3439 | |
| dc.identifier | http://arxiv.org/abs/0808.3439 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167716 | |
| dc.subject | Combinatorics | |
| dc.subject | 05E99 | |
| dc.title | Combinatorial bases for multilinear parts of free algebras with double compatible brackets | |
| dc.type | text |