On the centers of quantum groups of A(n)-type

Abstract Let g be the finite dimensional simple Lie algebra of type An, and let U = Uq(g, Λ) and U = Uq(g, Q) be the quantum groups defined over the weight lattice and over the root lattice, respectively. In this paper, we find two algebraically independent central elements in U for all n > 2 and give an explicit formula of the Casimir elements for the quantum group U = Uq(g, Λ), which corresponds to the Casimir element of the enveloping algebra U(g). Moreover, for n = 2 we give explicitly the generators of the center subalgebras of the quantum groups U = Uq(g, Λ) and U = Uq(g, Q).

Publication year:2018

Keywords:center, quantum group, type An, Casimir element

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BOF-publication weight:1

CSS-citation score:1

Authors:International

Authors from:Higher Education

Accessibility:Open