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- W560097931 abstract "The equitable presentation of $U_q(mathfrak{sl}_2)$ was introduced in 2006 by Ito, Terwilliger, and Weng. This presentation involves some generators $x, y, y^{-1}, z$. It is known that ${x^r y^s z^t : r, t in mathbb{N}, s in mathbb{Z}}$ is a basis for the $mathbb{K}$-vector space $U_q(mathfrak{sl}_2)$. In 2013, Bockting-Conrad and Terwilliger introduced a subalgebra $mathcal{A}$ of $U_q(mathfrak{sl}_2)$ spanned by the elements ${x^r y^s z^t : r, s, t in mathbb{N}, r+s+t {rm even}}$. We give a presentation of $mathcal{A}$ by generators and relations. We also classify up to isomorphism the finite-dimensional irreducible $mathcal{A}$-modules, under the assumption that $q$ is not a root of unity." @default.
- W560097931 created "2016-06-24" @default.
- W560097931 creator A5064653227 @default.
- W560097931 date "2015-06-05" @default.
- W560097931 modified "2023-09-27" @default.
- W560097931 title "The positive even subalgebra of $U_q(mathfrak{sl}_2)$ and its finite-dimensional irreducible modules" @default.
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