Nilpotent Lie and Leibniz Algebras

DOI10.1080/00927872.2012.717655zbMath1306.17001arXiv1207.3739OpenAlexW2075369419WikidataQ57442327 ScholiaQ57442327MaRDI QIDQ5412085

Alexander Combs, John T. Hird, Laurie Zack, Chelsie Batten Ray, Nicole A. Gin, Allison McAlister

Publication date: 25 April 2014

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.3739

zbMATH Keywords

Leibniz algebrasnilpotent Lie algebrasCartan subalgebrasFrattini subalgebras

Mathematics Subject Classification ID

Solvable, nilpotent (super)algebras (17B30) Leibniz algebras (17A32)

Related Items (21)

Relationships between factors of canonical central series of Leibniz algebras ⋮ Characterizing nilpotent Leibniz algebras by a new bound on their second homologies ⋮ Unnamed Item ⋮ Leibniz algebras with low-dimensional maximal Lie quotients ⋮ Leibniz \(A\)-algebras ⋮ Complex cyclic Leibniz superalgebras ⋮ Leibniz Algebras with Invariant Bilinear Forms and Related Lie Algebras ⋮ Classifying several classes of Leibniz algebras ⋮ Minimal nonnilpotent Leibniz algebras ⋮ Solvable extensions of the naturally graded quasi-filiform Leibniz algebra of second typeℒ² ⋮ A characterization of finite dimensional nilpotent Filippov algebras ⋮ Frattini Properties and Nilpotency in Leibniz Algebras ⋮ Solvable extensions of naturally graded quasi-filiform Leibniz algebras of second type ℒ¹ and ℒ³ ⋮ Poisson brackets, Novikov-Leibniz structures and integrable Riemann hydrodynamic systems ⋮ The second relative homology of Leibniz algebras ⋮ Some necessary and sufficient conditions for nilpotent n-Lie superalgebras ⋮ On classification of (n + 6)-dimensional nilpotent n-Lie algebras of class 2 with n ≥ 4 ⋮ Some radicals, Frattini and Cartan subalgebras of Leibnizn-algebras ⋮ On the subalgebra lattice of a Leibniz algebra ⋮ On Leibniz algebras with maximal cyclic subalgebras ⋮ Right and left solvable extensions of an associative Leibniz algebra

Cites Work

• Unnamed Item
• Jacobson's refinement of Engel's theorem for Leibniz algebras
• A Nonembedding theorem of nilpotent Lie algebras
• Some characterizations of nilpotent Lie algebras
• On Engel's Theorem for Leibniz Algebras
• Some Theorems on Leibniz Algebras
• ON NILPOTENT AND SIMPLE LEIBNIZ ALGEBRAS
• On Nilpotent Properties of Leibniz Algebras
• On nilpotent Lie algebras

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