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- W2912597457 abstract "A quantum symmetric pair consists of a quantum group $mathbf U$ and its coideal subalgebra ${mathbf U}^{imath}_{boldsymbol{varsigma}}$ with parameters $boldsymbol{varsigma}$ (called an $imath$quantum group). We initiate a Hall algebra approach for the categorification of $imath$quantum groups. A universal $imath$quantum group $widetilde{mathbf U}^{imath}$ is introduced and ${mathbf U}^{imath}_{boldsymbol{varsigma}}$ is recovered by a central reduction of $widetilde{mathbf U}^{imath}$. The semi-derived Ringel-Hall algebras of the first author and Peng, which are closely related to semi-derived Hall algebras of Gorsky and motivated by Bridgeland's work, are extended to the setting of 1-Gorenstein algebras, as shown in Appendix A by the first author. A new class of 1-Gorenstein algebras (called $imath$quiver algebras) arising from acyclic quivers with involutions is introduced. The semi-derived Ringel-Hall algebras for the Dynkin $imath$quiver algebras are shown to be isomorphic to the universal quasi-split $imath$quantum groups of finite type. Monomial bases and PBW bases for these Hall algebras and $imath$quantum groups are constructed." @default.
- W2912597457 created "2019-02-21" @default.
- W2912597457 creator A5034605545 @default.
- W2912597457 creator A5059827958 @default.
- W2912597457 date "2019-01-31" @default.
- W2912597457 modified "2023-09-27" @default.
- W2912597457 title "Hall algebras and quantum symmetric pairs I: foundations" @default.
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- W2912597457 doi "https://doi.org/10.48550/arxiv.1901.11446" @default.
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