相应于Borcherds-Cartan矩阵的双参数弱Hopf代数

Two-Parameter Weak Hopf Algebras Corresponding to Borcherds-Cartan Matrix

中文关键词:  Kac-Moody代数  弱反极  Borcherds-Cartan 矩阵.

英文关键词:Kac-Moody algebras  weak antipode  Borcherds-Cartan matrix.

中文摘要:

      本文构造了一类相应于Borcherds-Cartan 矩阵的双参数弱Hopf代数,这类是由非可换非余可换的弱Hopf代数组成,但它不是Hopf代数.这类弱Hopf代数可以被看作是单参弱Hopf代数 的推广.

英文摘要:

      In this paper a class of two-parameter weak Hopf algebras $w_{r,s}^{\tau}({\mathfrak g})$ corresponding to Borcherds-Cartan matrix is constructed. This class consists of noncommutative and noncocommutative weak Hopf algebras but not Hopf algebras. It can be viewed as a generalized class of one-parameter weak Hopf algebras $wU_q({\mathfrak g})$.