相关论文: Poisson-Lie Odd Bracket on Grassmann Algebra
A linear odd Poisson bracket realized solely in terms of Grassmann variables is suggested. It is revealed that with the bracket, corresponding to a semi-simple Lie group, both a Grassmann-odd Casimir function and invariant (with respect to…
A linear odd Poisson bracket (antibracket) realized solely in terms of Grassmann variables is suggested. It is revealed that the bracket, which corresponds to a semi-simple Lie group, has at once three Grassmann-odd nilpotent $\Delta$-like…
The paper has been withdrawn by the author.
A linear degenerate odd Poisson bracket (antibracket) realized solely on Grassmann variables is presented. It is revealed that this bracket has at once three nilpotent $\Delta$-like differential operators of the first, the second and the…
This paper has been withdrawn by the author due to incomplete interpretation for the results.
The general expression for the bicovariant bracket for odd generators of the external algebra on a Poisson-Lie group is given. It is shown that the graded Poisson-Lie structures derived before for $GL(N)$ and $SL(N)$ are the special cases…
Hartwig, Larsson and the second author in [J. Algebra, 2005] defined a bracket on sigma-derivations of a commutative algebra. We show that this bracket preserves inner derivations, and based on this obtain some structural results on…
This paper has been withdrawn by the author due to serious flaws in certain proofs. For instance, the method used to construct certain automorphic representations is flawed.
The paper is devoted to the Poisson brackets compatible with multiplication in associative algebras. These brackets are shown to be quadratic and their relations with the classical Yang--Baxter equation are revealed. The paper also contains…
In this paper we investigate Poisson-Lie transformation of dilaton and vector field J appearing in Generalized Supergravity Equations. While the formulas appearing in literature work well for isometric sigma models, we present examples for…
This paper has been withdrawn by the authors because it has been combined with "Higher Auslander Algebras Admitting Trivial Maximal Orthogonal Subcategories" (arXiv:0903.0761) together. Please see the new version of the latter paper for the…
The Grassmann-odd Nambu-like bracket corresponding to an arbitrary Lie algebra and realized on the Grassmann algebra is proposed.
This paper has been withdrawn by the author(s), due the final version in math.QA/0604564
This paper has been withdrawn by the author.
This paper has been withdrawn by the author.
This paper has been withdrawn by the author due to that the main results and approaches are closedly parallel to the ones in Lie algebra case.
The paper was withdrawn because of its significant overlap with a paper appeared recently.
The Grassmann-odd Nambu bracket on the Grassmann algebra is proposed.
The relation between Poisson brackets in supersymmetric one or two-dimensional sigma-models and derived brackets is summarized.
We study the Zariski cancellation problem for Poisson algebras in three variables. In particular, we prove those with Poisson bracket either being quadratic or derived from a Lie algebra are cancellative. We also use various Poisson algebra…