On the degenerations of solvable Leibniz algebras
J. M. CasasDepartment of Applied Mathematics I, E. E. Forestal, University of Vigo, 36005 Pontevedra, SpainAbror KhudoyberdiyevInstitute of Mathematics, National University of Uzbekistan, Tashkent 100125, UzbekistanM. LadraDepartment of Algebra, University of Santiago de Compostela, 15782 Santiago de Compostela, SpainB. A. OmirovInstitute of Mathematics, National University of Uzbekistan, Tashkent 100125, Uzbekistan
ABI
Abstract
The present paper is devoted to the description of rigid solvable Leibniz algebras. In particular, we prove that solvable Leibniz algebras under some conditions on the nilradical are rigid and we describe four-dimensional solvable Leibniz algebras with three-dimensional rigid nilradical. We show that the Grunewald-O'Halloran's conjecture "any $n$-dimensional nilpotent Lie algebra is a degeneration of some algebra of the same dimension" holds for Lie algebras of dimensions less than six and for Leibniz algebras of dimensions less than four. The algebra of level one, which is omitted in the 1991 Gorbatsevich's paper, is indicated.
Topics
Identifiers
Citations and references
Cited by 016 references
Metrics — AkademScholar · Coming soon