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Journal of Lie Theory 30 (2020), No. 4, 1117--1129
Copyright Heldermann Verlag 2020

On the Polynomial Realization of the Reduced W-Algebra Uχ(sl2,e)

Yang Zeng
School of Statistics and Mathematics, Nanjing Audit University, 211815 Nanjing, P. R. China

Hao Chang
School of Mathematics and Statistics, Central China Normal University, 430079 Wuhan, P. R. China


We study the structure of the reduced $W$-algebra $U_\chi(\mathfrak{sl}_2,e)$ with $e$ being regular nilpotent, over an algebraically closed field $k$ of characteristic $p>2$. As a consequence, we give a description of the center of the reduced enveloping algebra $U_\chi(\mathfrak{sl}_2)$.

Keywords: Center, regular nilpotent, reduced W-algebra, reduced enveloping algebra.

MSC: 17B50, 17B05, 17B35.

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