A fundamental representation of quantum generalized Kac-Moody algebras with one imaginary simple root  

作　　者：Jiangrong CHEN Zhonghua ZHAO 

机构地区：[1]School of Statistics, Capital University of Economics and Business, Beijing 100070, China [2]Department of Mathematics and Computer Science, School of Science,Beijing University of Chemical Technology, Beijing 100029, China

出　　处：《Frontiers of Mathematics in China》2015年第5期1041-1056,共16页中国高等学校学术文摘·数学（英文）

基　　金：The authors would like suggestions and express their sincere gratitude valuable discussion. The second author （Zhao） Natural Science Foundation of China （Grant No. Funds for the Central Universities. to thank the referees for many helpful to Professor Bangming Deng for many was partially supported by the National 11226063） and the Fundamental Research

摘　　要：We consider the Borcherds-Cartan matrix obtained from a symmetrizable generalized Cartan matrix by adding one imaginary simple root. We extend the result of Gebert and Teschner [Lett. Math. Phys., 1994, 31： 327-334] to the quantum case. Moreover, we give a connection between the irreducible dominant representations of quantum Kac-Moody algebras and those of quantum generalized Kac-Moody algebras. As the result, a large class of irreducible dominant representations of quantum generalized Kac-Moody algebras were obtained from representations of quantum Kac-Moody algebras through tensor algebras.We consider the Borcherds-Cartan matrix obtained from a symmetrizable generalized Cartan matrix by adding one imaginary simple root. We extend the result of Gebert and Teschner [Lett. Math. Phys., 1994, 31： 327-334] to the quantum case. Moreover, we give a connection between the irreducible dominant representations of quantum Kac-Moody algebras and those of quantum generalized Kac-Moody algebras. As the result, a large class of irreducible dominant representations of quantum generalized Kac-Moody algebras were obtained from representations of quantum Kac-Moody algebras through tensor algebras.

关 键 词：Quantum generalized Kac-Moody algebra tensor algebra fundamental representation 

分 类 号：O152.5[理学—数学] O413[理学—基础数学]