
Journal of Lie Theory 30 (2020), No. 4, 11171129 Copyright Heldermann Verlag 2020 On the Polynomial Realization of the Reduced WAlgebra U_{χ}(sl_{2},e) Yang Zeng School of Statistics and Mathematics, Nanjing Audit University, 211815 Nanjing, P. R. China zengyang214@163.com Hao Chang School of Mathematics and Statistics, Central China Normal University, 430079 Wuhan, P. R. China chang@mail.ccnu.edu.cn [Abstractpdf] 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 Walgebra, reduced enveloping algebra. MSC: 17B50, 17B05, 17B35. [ Fulltextpdf (154 KB)] for subscribers only. 