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

作者：Chen, Jiangrong; Zhao, Zhonghua^*

来源：Frontiers of Mathematics in China, 2015, 10(5): 1041-1056.

DOI：10.1007/s11464-015-0471-1

• Quantum generalized Kac-Moody algebra
• tensor algebra
• fundamental representation

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.

• 出版日期2015-10
• 单位北京化工大学; 首都经济贸易大学