Related papers: Poisson-Lie Odd Bracket on Grassmann Algebra
This paper has been removed by arXiv administrators because it plagiarizes hep-th/0311050, gr-qc/0306101, gr-qc/9601044, gr-qc/0511106, gr-qc/0303034, and gr-qc/0212018.
This paper has been withdrawn by the author due a few mistakes in the paper.
This paper is withdrawn by the author. See math.GT/9811093 for replacement.
This paper has been withdrawn by the author due to an error in Lemma 3, making the (bijective) proof of Theorem 4 and Corollary 5 invalid (symmetry of k-nonnesting and k-noncrossing set partitions).
The Grassmann-odd Nambu-like brackets corresponding to an arbitrary Lie superalgebra and realized on the supermanifolds are proposed.
This paper has been withdrawn by the author due to a misunderstanding.
This paper was withdrawn by the authors.
In this article we give corrections and addendum to the article ``Flops and Poisson deformations of symplectic varieties, Publ. Res. Inst. Math. Sci. {\bf 44} (2008) 259 - 314''.
In this paper, we determine the isomorphism classes of the central simple Poisson algebras introduced earlier by the second author. The Lie algebra structures of these Poisson algebras are in general not finitely-graded.
Let $A=F[x,y]$ be the polynomial algebra on two variables $x,y$ over an algebraically closed field $F$ of characteristic zero. Under the Poisson bracket, $A$ is equipped with a natural Lie algebra structure. It is proven that the maximal…
This paper was withdrawn by the authors. The mistake in math.AG/0209223 affects also this paper.
This paper has been withdrawn
One may introduce at least three different Lie algebras in any Lagrangian field theory : (i) the Lie algebra of local BRST cohomology classes equipped with the odd Batalin-Vilkovisky antibracket, which has attracted considerable interest…
The paper is withdrawn by the authors and replaced be an improved and extended version arxiv: 0812.2968
This paper has been withdrawn by the author due to rewritting and skipping crucial sign errors.
This paper has been withdrawn by the authors
We describe all Poisson brackets compatible with the natural cluster algebra structure in the open Schubert cell of the Grassmannian $G_k(n)$ and show that any such bracket endows $G_k(n)$ with a structure of a Poisson homogeneous space…
A general construction of an sh Lie algebra from a homological resolution of a Lie algebra is given. It is applied to the space of local functionals equipped with a Poisson bracket, induced by a bracket for local functions along the lines…
This paper has been withdrawn by the author due to a crucial error in the proof of Lemma 2.2.
The paper has been withdrawn