Combinatorial Bases for Multilinear Parts of Free Algebras with Double Compatible Brackets
نویسنده
چکیده
Let X be an ordered alphabet. L ie2(n) (and P2(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 L ie2(n) (and P2(n)) from combinatorial objects. We also define a complementary space E il2(n) to L ie2(n), give a pairing between L ie2(n) and E il2(n), and show that the pairing is perfect.
منابع مشابه
Combinatorial bases for multilinear parts of free algebras with two compatible brackets
Article history: Received 31 October 2008 Available online 28 October 2009 Communicated by Vera Serganova
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