Abstract
Based on the n-fold tensor product version of the generalized double-bosonization construction, we prove the Majid conjecture of the quantum Kac-Moody algebras version. Particularly, we give explicitly the double-bosonization type-crossing constructions of quantum Kac-Moody algebras for affine types \(G_2^{(1)}\), \(E_6^{(1)}\), and Tp,q,r, and in this way, we can recover generators of quantum Kac-Moody algebras with braided groups defined by R-matrices in the related braided tensor category. This gives us a better understanding for the algebra structures themselves of the quantum Kac-Moody algebras as a certain extension of module-algebras/module-coalgebras with respect to the related quantum subalgebras of finite types inside.
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Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11801394, 11771142, 11871249) and the Science and Technology Commission of Shanghai Municipality (No. 18dz2271000).
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Hu, H., Hu, N. & Xia, L. Majid conjecture: quantum Kac-Moody algebras version. Front. Math. China 16, 727–747 (2021). https://doi.org/10.1007/s11464-021-0905-x
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DOI: https://doi.org/10.1007/s11464-021-0905-x