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Majid conjecture: quantum Kac-Moody algebras version
Hongmei HU, Naihong HU, Limeng XIA
Front. Math. China. 2021, 16 (3): 727-747.
https://doi.org/10.1007/s11464-021-0905-x
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 , ,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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Transversality on locally pseudocompact groups
Fucai LIN, Zhongbao TANG
Front. Math. China. 2021, 16 (3): 771-782.
https://doi.org/10.1007/s11464-021-0940-7
Two non-discrete Hausdorff group topologies and on a group G are called transversal if the least upper bound of and is the discrete topology. In this paper, we discuss the existence of transversal group topologies on locally pseudocompact, locally precompact, or locally compact groups. We prove that each locally pseudocompact, connected topological group satisfies central subgroup paradigm, which gives an affrmative answer to a problem posed by Dikranjan, Tkachenko, and Yaschenko [Topology Appl., 2006, 153:3338-3354]. For a compact normal subgroup K of a locally compact totally disconnected group G, if G admits a transversal group topology, then G/K admits a transversal group topology, which gives a partial answer again to a problem posed by Dikranjan, Tkachenko, and Yaschenko in 2006. Moreover, we characterize some classes of locally compact groups that admit transversal group topologies.
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13 articles
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