Abstract
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.
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Chen, J., Zhao, Z. A fundamental representation of quantum generalized Kac-Moody algebras with one imaginary simple root. Front. Math. China 10, 1041–1056 (2015). https://doi.org/10.1007/s11464-015-0471-1
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DOI: https://doi.org/10.1007/s11464-015-0471-1