The Betti numbers for a family of solvable Lie algebras

2014/04/20 by Minh Thanh Duong, Duong, Minh Thanh
Chemistry · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Axial and Atropisomeric Chirality Synthesis #math.RA #msc:16W25 #msc:17B30 #msc:17B56 #msc:22E40

paper · pdf · doi:10.48550/arxiv.1404.5023

9 pages

arxiv created 2014/04/20 · arxiv updated 2014/04/22

Abstract

We give a characterization of symplectic quadratic Lie algebras that their Lie algebra of inner derivations has an invertible derivation. A family of symplectic quadratic Lie algebras is introduced to illustrate this situation. Finally, we calculate explicitly the Betti numbers of a family of solvable Lie algebras in two ways: using the cohomology of quadratic Lie algebras and applying a Pouseele's result on extensions of the one-dimensional Lie algebra by Heisenberg Lie algebras

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