2019/03/27 by Cao Trần Tứ Hải, Hai, Cao Tran Tu, Dương Minh Thành +3
Mathematics · #16E40 (Primary) #16W25 (Secondary) #17B30 #17B56 #17B60 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1903.11537
openalex publication_date 2019/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper studies the cohomology of Lie algebras and quadratic Lie algebras. Firstly, we propose to describe the cohomology of MD(n,1)-class which was introduced in \citeLHNCN16. This class contains Heisenberg Lie algebras. In 1983, L. J. Santharoubane \citeSan83 computed the cohomology of Heisenberg Lie algebras. In this paper, we will completely describe the cohomology of the other ones of MD(n, 1)-class. Finally, we will be concerned about the cohomology of quadratic Lie algebras. In 1985, A. Medina and P. Revoy \citeMR85 computed the second Betti number of the generalized real diamond Lie algebras. We will compute in this paper the second Betti number of the generalized complex diamond Lie algebras by using the super-Poisson bracket.