Related papers: Poisson-Lie Odd Bracket on Grassmann Algebra
This paper has been withdrawn by the authors. Some of the arguments developed in the paper are erroneous. They will be rectified in a later publication.
This paper has been withdrawn by the author.
An error in the paper [J. Math. Phys. 43, 6343 (2002); math-ph/0207009] is corrected. Further explanation is given.
The paper has been withdrawn.
The Lie algebra of pseudodifferential symbols on the circle has a nontrivial central extension (by the ``logarithmic'' 2-cocycle) generalizing the Virasoro algebra. The corresponding extended subalgebra of integral operators generates the…
The Poisson-Lie sigma models over nonsemisimple low dimensional real Poisson-Lie groups are investigated. We find two sided models on two, three and some four dimensional Poisson-Lie groups where the Poisson-Lie sigma models over…
M. Boucetta introduced the notion of pseudo-Riemannian Lie algebra in [2] when he studied the line Poisson structure on the dual of a Lie algebra. In this paper, we redefine pseudo-Riemannian Lie algebra, which, in essence, is a class of…
We study the general form of the *-commutator treated as a deformation of the Poisson bracket on the Grassman algebra. We show that, up to a similarity transformation, there are other deformations of the Poisson bracket in addition to the…
This paper has been withdrawn by the author due to a crucial error.
Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on R^n taking values in a Grassmann algebra are described up to an equivalence transformation. It is shown that there are additional…
This paper has been withdrawn due to crucial erros in equations (24)--(31).
It is well known that the Poisson Lie algebra is isomorphic to the Hamiltonian Lie algebra. We show that the Poisson Lie algebra can be embedded properly in the special type Lie algebra. We also generalize the Hamiltonian Lie algebra using…
This paper has been withdrawn by the author due to similarity to Author's other paper
The notion of Poisson manifold with compatible pseudo-metric was introduced by the author in [1]. In this paper, we introduce a new class of Lie algebras which we call a pseudo-Rieamannian Lie algebras. The two notions are strongly related:…
This paper has been withdrawn by the authors due to the existence of main results in the literature.
Major mistake. The paper has been withdrawn.
We study unital commutative associative algebras and their associated n-Lie algebras, showing that they are strong transposed Poisson n-Lie algebras under specific compatibility conditions. Furthermore, we generalize the simplicity…
This paper has been withdrawn by the author, due to a significant error in section 4.3.1.
The paper has been withdrawn.
This paper has been withdrawn by the author.