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Rigidity-preserving and cohomology-decreasing extensions of solvable rigid Lie algebras

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Ancochea Bermúdez, José María and Campoamor Stursberg, Otto Ruttwig (2017) Rigidity-preserving and cohomology-decreasing extensions of solvable rigid Lie algebras. Linear and Multilinear Algebra . pp. 1-15. ISSN 1563-5139 (In Press)

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Official URL: http://www.tandfonline.com/doi/full/10.1080/03081087.2017.1302404


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Abstract

It is shown that the two-known series of rank one (Formula presented.) and rank two (Formula presented.) finite-dimensional solvable rigid Lie algebras with non-vanishing second cohomology can be extended to solvable rigid Lie algebras of arbitrary rank (Formula presented.) such that the cohomology is preserved exactly. For the second series, it is further proved that an extension decreasing the cohomology exists, hence leading to cohomologically rigid Lie algebras.


Item Type:Article
Uncontrolled Keywords:Chevalley cohomology; Lie algebra; Quadratic Rim map; Rigidity; Solvable extension
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:42837
Deposited On:22 May 2017 10:01
Last Modified:12 Dec 2018 15:12

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