Completeness of quasi-filiform Lie algebras
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2013
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Taylor & Francis
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Almaraz Luengo, E. S., Ancochea Bermúdez, J. M. & García Vergonolle, L. «Completeness of Quasi-Filiform Lie Algebras». Linear and Multilinear Algebra, vol. 61, n.o 5, mayo de 2013, pp. 582-95. DOI.org (Crossref), https://doi.org/10.1080/03081087.2012.696250.
Almaraz Luengo, E. S., Ancochea Bermúdez, J. M. & García Vergnolle, L. «Completeness of Quasi-Filiform Lie Algebras». Linear and Multilinear Algebra, vol. 61, n.o 5, mayo de 2013, pp. 582-95. DOI.org (Crossref), https://doi.org/10.1080/03081087.2012.696250.
Almaraz Luengo, E. S., Ancochea Bermúdez, J. M. & García Vergnolle, L. «Completeness of Quasi-Filiform Lie Algebras». Linear and Multilinear Algebra, vol. 61, n.o 5, mayo de 2013, pp. 582-95. DOI.org (Crossref), https://doi.org/10.1080/03081087.2012.696250.
Abstract
It is proved that for any quasi-filiform of non-zero rank the solvable Lie algebra obtained by adjoining a maximal torus of outer derivations is complete. Further, for any positive integer m, it is shown that there exist solvable complete Lie algebras with the second ChevalleyEilenberg cohomology group of arbitrary dimension.