Related papers: A Survey on Nambu-Poisson Brackets

We show that one can skip the skew-symmetry assumption in the definition of Nambu-Poisson brackets. In other words, a n-ary bracket on the algebra of smooth functions which satisfies the Leibniz rule and a n-ary version of the Jacobi…

Nambu proposed an extension of dynamical system through the introduction of a new bracket (Nambu bracket) in 1973. This article is a short review of the developments after his paper. Some emphasis are put on a viewpoint that the Nambu…

We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.

In this survey we overview known results and get several new results on digraph compositions which generalize several classes of digraphs, such as quasi-transitive digraphs. After an introductory section, the paper is divided into six…

We consider a special type of self-similar sets, called fractal squares, and give a brief review on recent results and unsolved issues with an emphasis on their topological properties.

In this paper, we investigate some properties of generalized Fibonacci quaternions and Fibonacci-Narayana quaternions.

We give a variant of the Beauville--Narasimhan--Ramanan correspondence for irregular parabolic Higgs bundles with semi-simple irregular part and show that it defines a Poisson isomorphism between certain irregular Dolbeault moduli spaces of…

A survey written for the upcoming "Handbook of Enumerative Combinatorics".

Poisson algebras have become an essential topic in mathematics with a rich structure and wide applicability. Despite numerous resources available on Poisson structures, the algebraic side of the story remains relatively less explored. This…

We investigate orthogonal and symplectic bundles with parabolic structure, over a curve.

This is a survey on coarse geometry with an emphasis on coarse homology theories.

Using the effective Lagrangian approach, we clarify general issues about Nambu-Goldstone bosons without Lorentz invariance. We show how to count their number and study their dispersion relations. Their number is less than the number of…

Tempered distributions on Rn that have the Poisson structure are characterized in terms of geometry of its support and spectrum

This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature, and in which rational homogeneous spaces play a prominent r{\^o}le. This selection is largely…

This is a survey of results in the enumeration of lattice paths.

This is a survey paper: we discuss certain recent results, with some improvements. It will appear in the S. Cruz proceedings.

The paper contains enumerative combinatorics for positive braids, square free braids, and simple braids, emphasizing connections with classical Fibonacci sequence. The simple subgraph of the Cayley graph of the braid group is analyzed in…

We investigate the geometric interpretation of quantized Nambu-Poisson structures in terms of noncommutative geometries. We describe an extension of the usual axioms of quantization in which classical Nambu-Poisson structures are translated…

In this paper we introduce poly-Poisson structures as a higher-order extension of Poisson structures. It is shown that any poly-Poisson structure is endowed with a polysymplectic foliation. It is also proved that if a Lie group acts…

This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead…