Related papers: Poisson-Lie Odd Bracket on Grassmann Algebra

This paper has been withdrawn

This short note is an announcement of results. We continue the study of Yangian-type algebras initiated in the paper arXiv:2208.04809. These algebras share a number of properties of the Yangians of type A but are more massive. We refine and…

We introduce Poisson double algebroids, and the equivalent concept of double Lie bialgebroid, which arise as second-order infinitesimal counterparts of Poisson double groupoids. We develop their underlying Lie theory, showing how these…

Given a symplectic form and a pseudo-riemannian metric on a manifold, a non degenerate even Poisson bracket on the algebra of differential forms is defined and its properties are studied. A comparison with the Koszul-Schouten bracket is…

This paper has been withdrawn due to the adherance to the double submission policies of a refereed journal. Our apologies.

This paper has been withdrawn by the author(s), due a crucial i-number error in Eqn. 18.

This paper has been withdrawn by the author due to a crucial errors.

This paper has been withdrawn by the author.

The purpose of this paper is to propose a version of the notion of convenient Lie groupoid as a generalization of this concept in finite dimension. The authors point out which obstructions appear in the infinite dimensional context and how…

This paper has been withdrawn by the author because overcame by arXiv:0910.4694

We look for 3-dimensional Poisson-Lie dualizable sigma models that satisfy the vanishing beta-function equations with constant dilaton field. Using the Poisson-Lie T-plurality we then construct 3-dimensional sigma models that correspond to…

In field theory the Poisson bracket $\{F, \mathcal{H}\}$ between an arbitrary function $F$ and the system Hamiltonian $\mathcal{H}$ acquires odd contributions. Here a modification is worked out to remove those terms, which leads to a…

Withdrawn due to extensions and submission as another paper.

This paper has been withdrawn by the author due to an error in section 7. There is a new version: arXiv:1011.3352.

This paper has been withdrawn by the author; a revised version is part of the author's phd-thesis "Quasi-logarithmic structures" (Zurich, 2007).

Let a Lie algebra $\mathfrak q$ be a linear sum of two complementary subalgebras $\mathfrak h$ and $\mathfrak r$. We continue our investigations initiated in (J. London Math. Soc. 103 (2021), 1577-1595), where compatible Poisson brackets…

We consider odd Poisson (odd symplectic) structure on supermanifolds induced by an odd symmetric rank $2$ (non-degenerate) contravariant tensor field. We describe the difference between odd Riemannian and odd symplectic structure in terms…

We develop here a simple quantisation formalism that make use of Lie algebra properties of the Poisson bracket. When the brackets $\{H,\phi_i\}$ and $\{\phi_i,\phi_j\}$, where $H$ is the Hamiltonian and $\phi_i$ are primary and secondary…

This paper has being withdrawn by the authors due to an error in the conclusion.

This paper has been withdrawn as the statements in Proposition 4.4 and Theorem 1.4(i) are not correct.