Cohomology of ℕ-graded Lie algebras of maximal class over ℤ₂

2015/12/24 by Yuri Nikolayevsky, Nikolayevsky, Yuri, Ioannis Tsartsaflis +1
Mathematics · #17B30 #17B50 #17B56 #17B65 #17B70 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1512.07676

openalex publication_date 2015/12/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We compute the cohomology with trivial coefficients of Lie algebras \mathfrakm₀ and \mathfrakm₂ of maximal class over the field ℤ₂. In the infinite-dimensional case, we show that the cohomology rings H^*(\mathfrakm₀) and H^*(\mathfrakm₂) are isomorphic, in contrast with the case of the ground field of characteristic zero, and we obtain a complete description of them. In the finite-dimensional case, we find the first three Betti numbers of \mathfrakm₀(n) and \mathfrakm₂(n) over ℤ₂.

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• Cohomology of graded Lie algebras of maximal class
• Adjoint cohomology of graded Lie algebras of maximal class
• Cohomology of some families of Lie algebras and quadratic Lie algebras
• Graded Lie algebras of maximal class IV
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