Journal of Lie Theory 31 (2021), No. 1, 015--028
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 H-pseudoalgebra W(m, π, g), which is a generalization of the vector field Lie H-pseudoalgebra W(g) defined earlier by B. Bakalov, A. D'Andrea and V. G. Kac [Theory of finite pseudoalgebras, Advances in Mathematics 162(1) (2001) 1--140]. We prove that automorphisms of W(m, π, g) are in one-to-one correspondence with solutions of some Maurer-Cartan equation when g is a finite dimensional simple Lie algebra.
Keywords: Lie pseudoalgebra, singular vector, Maurer-Cartan equation.
MSC: 17B30, 17B68, 17B99; 16S99.
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