Leibniz Algebras

By Sh. A. Ayupov, Bakhrom Omirov. 2019

171 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/65561f9e3a1c0ccf06d912cb664b8cfbce7810e1

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Quasi, twisted, and all that... in Poisson geometry and Lie algebroid theory (2003, background): “In [27], he and Kinyon explored this problem and initiated the search for the global objects associated to generalized Lie algebras, that would generalize Lie groups.”
Classification of solvable Leibniz algebras with null-filiform nilradical (2012, background): “〈x +N〉 is an ideal because of R(2) ⊆ N ; its nilpotency is argued as follows: if a ∈ N , then Ra is a nilpotent operator thanks to Engel’s theorem for Leibniz algebras [4]; since Rx| N is a nilpotent operator by assumption, then Ra +Rx| N is a nilpotent operator because of the formula (Ra +Rx| N ) =”
Relationships between factors of canonical central series of Leibniz algebras (2016, background): “Omirov [3] and continued in the papers [1,2,4,7,15,20], sometimes under different approaches.”
Reduction of Courant algebroids and generalized complex structures (2005, unknown): “This bracket appeared in [17], where it was called the hemisemidirect product of g with h.”
Classification of solvable Leibniz algebras with naturally graded filiform nilradical (2012, methodology): “The nilpotency of this ideal follows from the Engel’s theorem for Leibniz algebras [4].”
Leibniz Algebras, Lie Racks, and Digroups (2004, unknown): “Weinstein made an attempt to understand coquecigrues in [10] by using smooth, nonassociative multiplications defined on reductive homogeneous spaces that are associated to Leibniz algebras.”