弱Hopf代数的扭曲的Smash积及Smash余积

构筑了弱Hopf代数的扭曲的Smash积和Smash余积，并研究了它们的混合积，进一步证明了它们也是弱Hopf代数，最后，给出了这类弱Hopf代数（余）交换的充要条件。     

Comments on a paper by Marchildon,Antippa, and Everett about tachyons

Marchildonet al. [Phys. Rev. D 27, 1740 (1983)] expressed criticisms about old versions of some approaches to the theory of tachyons. We refute those criticisms somewhatbriefly, since suitable answers werealready present in the literature at the time when the paper here commented upon was being prepared.     

关于双对称余代数

通过研究双对称代数的对偶结构，主要讨论双对称余代数的张量积及双对称代数和双对称余代数之间的对偶关系。同时，也讨论了双对称双代数。     

Universal Differential Calculus on Ternary Algebras

General concept of ternary algebras is introduced in this article, along with several examples of its realization. Universal envelope of such algebras is defined, as well as the concept of tri-modules over ternary algebras. The universal differential calculus on these structures is then defined and its basic properties investigated.     

关于(余)反射的范畴性质及其应用

本文研究了（余）反射的范畴性质及应用，得到的主要结果如下：（１）余反射余代数范畴和反射代数范畴是等价的．（２）反射和余反射都具有可扩张性．使用这些结果可以用来推广和化简了［１—４］等人的部分工作．     

Characters of Simple Bounded Modules over an Untwisted Affine Lie Algebra

After V. Chari and A. Pressley, a simple integrable module with finite-dimensional weight spaces over an affine Lie algebra is either a standard module (highest or lowest weight), in which case its formal character is given by the famous Weyl–Kac formula, or a subquotient of a tensor product of loop modules. In this paper we compute formal characters of generic simple integrable modules of the latter type.     

Ramanujan's Master Theorem for Hermitian Symmetric Spaces

In this paper we generalize Ramanujan's Master Theorem to the context of a Siegel domain of Type II, which is the Hermitian symmetric space of a real non-compact semisimple Lie group of finite center. That is, the spherical transform of a spherical series can be expressed in terms of the coefficients of this series.     

整环上二阶线性李代数的自同构

设Ｒ是有１的交换环，２是Ｒ的单位．本文决定了Ｒ上李代数ｓｌ２（Ｒ）的理想．进而，若Ｒ是整环，本文决定了ｓｌ２（Ｒ）与ｇｌ２（Ｒ）的自同构形式．     

Vertex Algebras and Combinatorial Identities

In the 1980's, J. Lepowsky and R. Wilson gave a Lie-theoretic interpretation of Rogers–Ramanujan identities in terms of level 3 representations of affine Lie algebra sl(2,C)~. When applied to other representations and affine Lie algebras, Lepowsky and Wilson's approach yielded a series of other combinatorial identities of the Rogers–Ramanujan type. At about the same time, R. Baxter rediscovered Rogers–Ramanujan identities within the context of statistical mechanics. The work of R. Baxter initiated another line of research which yielded numerous combinatorial and analytic generalizations of Rogers–Ramanujan identities. In this note, we describe some ideas and results related to Lepowsky and Wilson's approach and indicate the connections with some results in combinatorics and statistical physics.     

The Triangulated Hopf Category n +SL(2)

We discuss an example of a triangulated Hopf category related to SL(2). It is an equivariant derived category equipped with multiplication and comultiplication functors and structure isomorphisms. We prove some coherence equations for structure isomorphisms. In particular, the Hopf category is monoidal.