Explicit generators of the centre of the quantum group
Yanmin Dai

TL;DR
This paper constructs explicit algebraically independent central elements for a generalized quantum group associated with a simple Lie algebra, proving that these generate its entire centre, which is a polynomial algebra.
Contribution
It introduces a set of explicit generators for the centre of a generalized quantum group and proves they form a polynomial algebra, utilizing a quantum Harish-Chandra isomorphism.
Findings
Centre of the generalized quantum group is a polynomial algebra.
Constructed explicit algebraically independent central elements.
Proved these elements generate the entire centre.
Abstract
For a slightly generalised version of the Jimbo quantum group associated with any finite dimensional simple Lie algebra , we show that its centre is a polynomial algebra. We construct a set of algebraically independent central elements, each associated with a fundamental weight of , and prove that they generate the entire centre of the quantum group. A key ingredient in the proofs of these results is a quantum Harish-Chandra isomorphism for the generalised quantum group, which is proven in some details.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons
