Two-Parameter Weak Hopf Algebras Corresponding to Borcherds-Cartan Matrix
Received:February 16, 2009  Revised:May 16, 2009
Key Words: Kac-Moody algebras   weak antipode   Borcherds-Cartan matrix.  
Fund Project:the National Natural Science Foundation of China (Nos.10671016; 10771014); the Foundation of Beijing Educational Committee (No.KM200710005013).
Author NameAffiliation
AI Chun Rui Department of Mathematics, Henan Normal University, Henan 453007, China 
YANG Shi Lin College of Applied Sciences, Beijing University of Technology, Beijing 100124, China 
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      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 $wU_q({\mathfrak g})$.
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