Quasi-triangular Hopf algebras and invariant Jacobians
Abstract
We show that two module homomorphisms for groups and Lie algebras established by Xi can be generalized to the setting of quasi-triangular Hopf algebras. These module homomorphisms played a key role in his proof of a conjecture of Yau (1998). They will also be useful in the problem of decomposition of tensor products of modules. Additionally, we give another generalization of result of Xi in terms of Chevalley-Eilenberg complex.
Keywords
quasi-triangular Hopf algebra universal R-matrix quantum group invariant JacobianMSC(2010)
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Notes
Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant No. 11501546). The author thanks Professor Nanhua Xi for his helpful suggestions and comments in writing this paper, and Professor Naihong Hu for his advice on references and comments. The author also thanks the referees for their careful reading and valuable suggestions to this paper.
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