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Low-dimensional non-abelian Leibniz cohomology
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José Manuel Casas
,
Emzar Khmaladze
Published/Copyright:
May 2, 2013
Abstract.
We construct the zero and first non-abelian cohomologies of Leibniz algebras with coefficients in crossed modules, which differ from those of Gnedbaye and generalize the zero and first Leibniz cohomologies of Loday and Pirashvili. We also introduce the second non-abelian Leibniz cohomology and describe its relationship with extensions of Leibniz algebras by crossed modules. We obtain a nine-term exact non-abelian cohomology sequence. For Lie algebras we compare the non-abelian Leibniz and Lie cohomologies.
Received: 2010-12-15
Published Online: 2013-05-02
Published in Print: 2013-05-01
© 2013 by Walter de Gruyter Berlin Boston
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Keywords for this article
Leibniz algebra;
crossed module;
non-abelian cohomology;
derivation and anti-derivation
Articles in the same Issue
- Masthead
- Low-dimensional non-abelian Leibniz cohomology
- Twisted torsion invariants and link concordance
- Groups with faithful irreducible projective unitary representations
- Universality of the Selberg zeta-function for the modular group
- An innocent theorem of Banaschewski, applied to an unsuspecting theorem of De Marco, and the aftermath thereof
- Knotted surfaces in 4-manifolds
- Knot surgery and Scharlemann manifolds
- On the Sato–Tate conjecture on average for some families of elliptic curves
