Character formulas for the operad of two compatible brackets and for the bi-Hamiltonian operad. (English. Russian original) Zbl 1145.18001
Funct. Anal. Appl. 41, No. 1, 1-17 (2007); translation from Funkts. Anal. Prilozh. 41, No. 1, 1-22 (2007).
This paper studies the operad of two compatible brackets and the bi-Hamiltonian operad. It starts with the concepts and preliminaries on related operads and their properties, including the Koszulness and Cohen-Macaulayness. Then the main theorem on characters is stated and proved, followed by discussions on monomial bases and decompositions. The proofs make use of the connections of Koszul operads with Cohen-Macaulay posets and with distributive lattices.
Reviewer: Li Guo (Newark)
MSC:
| 18D50 | Operads (MSC2010) |
| 20C30 | Representations of finite symmetric groups |
| 05E25 | Group actions on posets, etc. (MSC2000) |
| 06A11 | Algebraic aspects of posets |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
Keywords:
operad; bi-Hamiltonian algebra; compatible Poisson brackets; distributive law; Koszul operad; Cohen-Macaulay posetReferences:
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