Journal of Lie Theory 35 (2025), No. 1, 101--108
Copyright Heldermann Verlag 2025
Semisimple Algebras of Vector Fields on CN of Maximal Rank
Hassan Azad
Abdus Salam School of Mathematical Sciences, Lahore, Pakistan
hassan.azad@sms.edu.pk
Indranil Biswas
Dept. of Mathematics, Shiv Nadar University, Tehsil Dadri, Greater Noida, Uttar Pradesh, India
indranil.biswas@snu.edu.in
Fazal M. Mahomed
School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa
fazal.mahomed@wits.edu.za
A local classification of semisimple Lie algebras of vector fields on CN that have a Cartan subalgebra of dimension N is given. The proof uses basic representation theory and the local canonical form of semisimple Lie algebras of vector fields.
Keywords: Vector field, semisimple Lie algebra, Levi decomposition.
MSC: 17B66, 32M25, 57R25.
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