关于群胚作用和李双代数胚态射

在这篇文章中，我们讨论了李双代数胚之间的态射，得到了一些李双代数胚之间态射的性质．研究了泊松群胚在泊松流形上的泊松作用，以及这个泊松作用与被作用流形的切李双代数胚到作用泊松群胚的切李双代数胚之间的态射的关系，得到了一些有用的结论。     

函数恒等式理论在泊松超代数上的应用(英文)

泊松超代数既是结合超代数又是李超代数.本文利用结合超代数上的函数恒等式理论研究泊松超代数上的映射,将李超代数上的一类映射转化为结合超代数上的映射.     

群胚上的Dirac结构及泊松约化

本文详细讨论了李双代数胚中的Dirac结构、群胚上的Dirac结构。利用Dirac结构的特征对的概念,给出了作用不变Dirac结构,拉回Dirac结构等概念的新的刻画。最后利用Dirac结构的有关性质,讨论了泊松齐性空间和泊松群胚作用的约化。     

G匚W上的泊松群胚结构

从泊松作用的角度考察了群胚上的半直积结构,定义了泊松群胚对泊松群胚的泊松作用,讨论了其性质,并证明了两个泊松群胚的半直积仍是泊松群胚,从而对群胚的半直积结构有了更多的认识.     

直观实用的泊松图

本文介绍一种用来诊断数据是否来自泊松总体的方法—泊松图，并通过实例分析，说明诊断过程。     

着色李超代数与左着色对称结构

本文研究了着色李超代数上的左着色对称结构问题.利用着色李超代数的两种仿射表示和1-上同调群,得出左着色对称结构存在的几个充分或必要条件,推广了文[2]的结论.     

截尾平稳泊松过程及泊松流的分布

本文分析了区间〔０，＋∞〕上强度为λ（常数）的泊松过程的性质，提出了另一类新的模型－－截尾平稳泊松过程，得出了截尾平稳泊松过程的性质及泊松流的分布。     

关于李群胚和泊松作用的讨论

定义了纤维丛的相配群胚的概念,从作用的角度研究了李群胚与主丛的关系;给出了一个泊松群胚在泊松流形上的作用是泊松作用的充要条件;文末得到了一些关于泊松流形上Casimir函数的结果.     

复合泊松过程及其在保险风险中的若干应用

本文利用齐次泊松过程的可加性,研究了复合泊松过程的可加性及其性质。作为应用,讨论了单个理赔额服从指数分布的复合泊松风险模型在第n次索赔时发生负盈余的概率。     

复合泊松过程的可加性

对复合泊松分布可加性的研究在许多的文献中都可以看到,本文首先应用特征函数的方法证明了复合泊松分布的可加性.以此为基础,结合对随机过程相关性质的讨论,证明了复合泊松过程也具有与复合泊松分布可加性相似的,某种意义上的可加性性质.     

Poisson color algebras of arbitrary degree

A Poisson algebra is a Lie algebra endowed with a commutative associative product in such a way that the Lie and associative products are compatible via a Leibniz rule. If we part from a Lie color algebra, instead of a Lie algebra, a graded-commutative associative product and a graded-version Leibniz rule we get a so-called Poisson color algebra (of degree zero). This concept can be extended to any degree, so as to obtain the class of Poisson color algebras of arbitrary degree. This class turns out to be a wide class of algebras containing the ones of Lie color algebras (and so Lie superalgebras and Lie algebras), Poisson algebras, graded Poisson algebras, z-Poisson algebras, Gerstenhaber algebras, and Schouten algebras among other classes of algebras. The present paper is devoted to the study of structure of Poisson color algebras of degree g₀, where g₀ is some element of the grading group G such that g₀ = 0 or 4g₀≠0, and with restrictions neither on the dimension nor the base field, by stating a second Wedderburn-type theorem for this class of algebras.     

(Quasi-)Poisson enveloping algebras

We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equivalent to the category of left modules over its quasi-Poisson enveloping algebra, and the category of Poisson modules is equivalent to the category of left modules over its Poisson enveloping algebra.     

Universal Poisson Envelope for Binary-Lie Algebras

In this article the universal Poisson enveloping algebra for a binary-Lie algebra is constructed. Taking a basis 𝔹 of a binary-Lie algebra B, we consider the symmetric algebra S(B) of polynomials in the elements of 𝔹. We consider two products in S(B), the usual product of polynomials fg and the braces {f, g}, defined by the product in B and the Leibniz rule. This algebra is a general Poisson algebra. We find an ideal I of S(B) such that the factor algebra S(B)/I is the universal Poisson envelope of B. We provide some examples of this construction for known binary-Lie algebras.     

Toroidal李代数上的Poisson代数结构

非交换的Poisson代数同时具有结合代数和李代数两种代数结构,而结合代数和李代数之间满足所谓的Leibniz法则．文中确定了Toroidal李代数上所有的Poisson代数结构,推广了仿射Kac-Moody代数上相应的结论．     

Frobenius Poisson algebras

This paper is devoted to study Frobenius Poisson algebras. We introduce pseudo-unimodular Poisson algebras by generalizing unimodular Poisson algebras, and investigate Batalin-Vilkovisky structures on their cohomology algebras. For any Frobenius Poisson algebra, all Eatalin-Vilkovisky opera tors on its Poisson cochain complex are described explicitly. It is proved that there exists a Batalin-Vilkovisky operator on its cohomology algebra which is induced from a Batalin-Vilkovisky operator on the Poisson cochain complex, if and only if the Poisson st rue ture is pseudo-unimodular. The relation bet ween modular derivations of polynomial Poisson algebras and those of their truncated Poisson algebras is also described in some cases.     

Realization of Poisson enveloping algebra

For a Poisson algebra, the category of Poisson modules is equivalent to the module category of its Poisson enveloping algebra, where the Poisson enveloping algebra is an associative one. In this article, for a Poisson structure on a polynomial algebra S, we first construct a Poisson algebra R, then prove that the Poisson enveloping algebra of S is isomorphic to the specialization of the quantized universal enveloping algebra of R, and therefore, is a deformation quantization of R.     

扭Heisenberg-Virasoro代数上的Poisson结构

Poisson代数是指同时具有代数结构和李代数结构的一类代数,其乘法与李代数乘法满足Leibniz法则.扭Heisenberg-Virasoro代数是一类重要的无限维李代数,是次数不超过1的微分算子李代数W(0)的普遍中心扩张,与曲线的模空间有密切联系.本文主要研究扭Heisenberg-Virasoro代数上的Poisson结构,首先确定了李代数W(0)上的Poisson结构,进而给出了扭Heisenberg-Virasoro代数上的Poisson结构.     

Witt代数和Virasoro代数上的Poisson代数结构

Poisson代数是指同时具有结合代数结构和李代数结构的一类代数,其结合代数结构和李代数结构满足Leibniz法则.确定了特征为0和特征为p>0的基域上的Witt代数和Virasoro代数上的Poisson代数结构.     

Relationship Between Quantum and Poisson Structures of Odd Dimensional Euclidean Spaces

It is shown that the prime and primitive spectra of the multiparameter quantized algebra of odd-dimensional euclidean spaces are homeomorphic to the Poisson prime and Poisson primitive spectra of the multiparameter Poisson algebra of odd-dimensional euclidean spaces in the case when the multiplicative subgroup of a base field generated by the parameters is torsion free. As a corollary, it is shown that the prime and primitive spectra of the multiparameter quantized algebra of odd-dimensional euclidean spaces are topological quotients of the prime and maximal spectra of the corresponding commutative polynomial ring.     

Poisson manifolds with compatible pseudo-metric and pseudo-Riemannian Lie algebras

In a previous paper (C. R. Acad. Sci. Paris Sér. I 333 (2001) 763–768), the author introduced a notion of compatibility between a Poisson structure and a pseudo-Riemannian metric. In this paper, we introduce a new class of Lie algebras called pseudo-Riemannian Lie algebras. The two notions are closely related: we prove that the dual of a Lie algebra endowed with its canonical linear Poisson structure carries a compatible pseudo-Riemannian metric if and only if the Lie algebra is a pseudo-Riemannian Lie algebra. Moreover, the Lie algebra obtained by linearizing at a point a Poisson manifold with a compatible pseudo-Riemannian metric is a pseudo-Riemannian Lie algebra. We also give some properties of the symplectic leaves of such manifolds, and we prove that every Poisson manifold with a compatible Riemannian metric is unimodular. Finally, we study Poisson Lie groups endowed with a compatible pseudo-Riemannian metric, and we give the classification of all pseudo-Riemannian Lie algebras of dimension 2 and 3.