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Axioms 2019, 8(1), 10; https://doi.org/10.3390/axioms8010010

Some Features of Rank One Real Solvable Cohomologically Rigid Lie Algebras with a Nilradical Contracting onto the Model Filiform Lie Algebra Qn

1
Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, Plaza de Ciencias 3, E-28040 Madrid, Spain
2
Dpto de Geometría y Topología, Fac. CC. Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, E-28040 Madrid, Spain
*
Author to whom correspondence should be addressed.
Received: 25 November 2018 / Revised: 11 January 2019 / Accepted: 14 January 2019 / Published: 16 January 2019
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Abstract

The generic structure and some peculiarities of real rank one solvable Lie algebras possessing a maximal torus of derivations with the eigenvalue spectrum spec ( t ) = 1 , k , k + 1 , , n + k 3 , n + 2 k 3 for k 2 are analyzed, with special emphasis on the resulting Lie algebras for which the second Chevalley cohomology space vanishes. From the detailed inspection of the values k 5 , some series of cohomologically rigid algebras for arbitrary values of k are determined. View Full-Text
Keywords: real Lie algebra; solvable; rigidity; cohomology; contraction real Lie algebra; solvable; rigidity; cohomology; contraction
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Campoamor-Stursberg, R.; Oviaño García, F. Some Features of Rank One Real Solvable Cohomologically Rigid Lie Algebras with a Nilradical Contracting onto the Model Filiform Lie Algebra Qn. Axioms 2019, 8, 10.

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