一类超W-代数上的Poisson超结构

源于Poisson几何的Poisson代数同时具有代数结构和李代数结构,其乘法与李代数乘法满足Leibniz法则.超W-代数是复数域C上的无限维李超代数.主要研究一类超W-代数上的Poisson超结构.     

Quantizations of the W-Algebra W（2, 2）

We quantize the W-algebra W(2, 2), whose Verma modules, Harish-Chandra modules, irreducible weight modules and Lie bialgebra structures have been investigated and determined in a series of papers recently.     

Biderivations,linear commuting maps and commutative post-Lie algebra structures on W-algebras

In this paper, the biderivations without the skew-symmetric condition of W-algebras including the Witt algebra, the algebra W(2,2) and their central extensions are characterized. Some classes of non-inner biderivations are presented. As applications, the forms of linear commuting maps and the commutative post-Lie algebra structures on aforementioned W-algebras are given.     

有限W-代数与横截Poisson结构

证明了物理学中的有限Ｗ－代数是半单Ｌｉｅ代数上的横截Ｐｏｉｓｓｏｎ结构．     

Conjugacy classes in Weyl groups and q-W algebras

We define noncommutative deformations of algebras of regular functions on certain transversal slices to the set of conjugacy classes in an algebraic group G which play the role of Slodowy slices in algebraic group theory. The algebras called q-W algebras are labeled by (conjugacy classes of) elements s of the Weyl group of G. The algebra is a quantization of a Poisson structure defined on the corresponding transversal slice in G with the help of Poisson reduction of a Poisson bracket associated to a Poisson–Lie group G^? dual to a quasitriangular Poisson–Lie group. We also define a quantum group counterpart of the category of generalized Gelfand–Graev representations and establish an equivalence between this category and the category of representations of the corresponding q-W algebra. The algebras can be regarded as quantum group counterparts of W-algebras. However, in general they are not deformations of the usual W-algebras.     

Weil Representation and Metaplectic Groups over an Integral Domain

Given F a locally compact, nondiscrete, non-archimedean field of characteristic ≠ 2 and R an integral domain such that a non-trivial smooth character χ: F → R ^× exists, we construct the (reduced) metaplectic group attached to χ and R. We show that it is in the expected cases a double cover of the symplectic group over F. Finally, we define a faithful infinite dimensional R-representation of the metaplectic group analogue to the Weil representation in the complex case.