A Serre presentation for the $\imath$quantum covering groups
Christopher Chung

TL;DR
This paper extends Serre presentations to $ extit{i}$-quantum covering groups, incorporating a parameter $ extit{ extpi}$ that interpolates between Lusztig quantum groups and quantum supergroups, with new $ extit{ extpi}$-Serre relations.
Contribution
It generalizes Serre presentations to quantum covering algebras with an additional parameter, unifying quantum groups and supergroups within a single framework.
Findings
Established Serre presentation for $ extit{i}$-quantum covering groups.
Introduced $ extit{ extpi}$-Serre relations and $ extit{ extpi}$-divided powers.
Unified quantum groups and supergroups via a parameter $ extit{ extpi}$.
Abstract
Let be a quasi-split quantum symmetric pair of Kac-Moody type. The quantum group admits a Serre presentation featuring the -Serre relations in terms of -divided powers. Generalizing this result, we give a Serre presentation of quantum symmetric pairs for quantum covering algebras , which have an additional parameter that specializes to the Lusztig quantum group when and quantum supergroups of anisotropic type when . We give a Serre presentation for , introducing the -Serre relations and -divided powers.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry
