相关论文: A Survey on Nambu-Poisson Brackets

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…

There are various concepts of structure preserving mappings in geometry. It is the aim of the present paper to give a survey on geometrical characterizations of some of those mappings. We discuss the results for projective spaces in some…

We present some basic results on a natural Poisson structure on any compact symmetric space. The symplectic leaves of this structure are related to the orbits of the corresponding real semisimple group on the complex flag manifold.

In this paper, we introduce a new type fuzzy boundary and study some related set theoretic identities. Further, this new type of fuzzy boundary is compared with different existing fuzzy boundaries.

We give a brief introduction to some of the recent works on finding geometric structures on triangulated surfaces using variational principles.

This is a survey on stated skein algebras and their representations.

These lectures on the Batalin-Vilkovisky method of quantization were delivered at "VII Mexican School of Particles and Fields", M\'erida, M\'exico, October 30-November 6, 1996. In section II, we study the derivation of BV from…

We explore geometric and topological properties of 3d surfaces swept by Poncelet triangles, as well as tangles formed by associated points.

We introduce a relation of cobordism for knots in thickened surfaces and study cobordism invariants of such knots.

This paper describes some of the ideas used in the development of our work on small gaps between primes.

We give a brief survey of abelian torsions of 3-manifolds.

We consider a class of \textit{factorizable} Poisson brackets which includes almost all reasonable Poisson structures. A particular case of the factorizable brackets are those associated with symplectic Lie algebroids. The BRST theory is…

We show how the relation between Poisson brackets and symplectic forms can be extended to the case of inhomogeneous multivector fields and inhomogeneous differential forms (or pseudodifferential forms). In particular we arrive at a notion…

This is, mostly, a survey of results about the birational geometry of rationally connected manifolds, using rational curves analogous to lines in ${\mathbb P}^n$ ({\it quasi-lines}). Various characterizations of a Zariski neighbourhood of a…

This is a short survey paper, partly meant as a research announcement. Its purpose is to highlight some aspects of the interplay between quantales, inverse semigroups, and groupoids. Many of the results mentioned have not yet been presented…

In this paper we define a Poisson structure on some moduli spaces related to principal G-bundles on elliptic curves, the simplest example being the moduli space of stable pairs: a vector bundle and its global section. We also study…

We study the geometric structure of Poncelet $n$-gons from a projective point of view. In particular we present explicit constructions of Poncelet $n$-gons for certain $n$ and derive algebraic characterisations in terms of bracket…

The object of this paper is study $(\epsilon)$-para-Sasakian 3-manifolds satisfying certain conditions on the $\mathcal{Z}$ tensor. We characterize, $\mathcal{Z}$-symmetric; $\mathcal{Z}$-semisymmetric; $\mathcal{Z}$-pseudosymmetric; and…

This is a survey paper of the theory of crystal bases, global bases and the cluster algebra structure on the quantum coordinate rings.

This is a survey article on recent results on vector bundles on symmetric product of non-singular projective curves.