
Journal of Lie Theory 31 (2021), No. 1, 015028 Copyright Heldermann Verlag 2021 On the Lie Pseudoalgebra W(m, π, g) Maosen Xu School of Mathematics Sciences, Zhejiang University, Hangzhou 310027, P. R. China 390596169@qq.com Yan Tan College of Science, Zhejiang Agriculture and Forestry University, Hangzhou 311300, P. R. China ytanalg@126.com Zhixiang Wu School of Mathematics Sciences, Zhejiang University, Hangzhou 310027, P. R. China wzx@zju.edu.cn We investigate the structure and finite irreducible representation of a Lie Hpseudoalgebra W(m, π, g), which is a generalization of the vector field Lie Hpseudoalgebra W(g) defined earlier by B. Bakalov, A. D'Andrea and V. G. Kac [Theory of finite pseudoalgebras, Advances in Mathematics 162(1) (2001) 1140]. We prove that automorphisms of W(m, π, g) are in onetoone correspondence with solutions of some MaurerCartan equation when g is a finite dimensional simple Lie algebra. Keywords: Lie pseudoalgebra, singular vector, MaurerCartan equation. MSC: 17B30, 17B68, 17B99; 16S99. [ Fulltextpdf (148 KB)] for subscribers only. 