Abstract
We introduce a non-abelian exterior product of two crossed modules of Leibniz algebras and investigate its relation to the low-dimensional Leibniz homology. Later this non-abelian exterior product is applied to the construction of an eight term exact sequence in Leibniz homology. Also its relationship to the universal quadratic functor is established, which is applied to the comparison of the second Lie and Leibniz homologies of a Lie algebra.
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We would like to thank the anonymous referees for their comments and suggestions that helped us to improve this paper.
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The authors were supported by Ministerio de Economía y Competitividad (Spain) (European FEDER support included), Grant MTM2016-79661-P. The second author was also supported by Xunta de Galicia, Grant GRC2013-045 (European FEDER support included), by an FPU scholarship, Ministerio de Educación, Cultura y Deporte (Spain) and by a Fundación Barrié scolarship. The third author was supported by Shota Rustaveli National Science Foundation, Grant FR/189/5-113/14.
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Donadze, G., García-Martínez, X. & Khmaladze, E. A non-abelian exterior product and homology of Leibniz algebras. Rev Mat Complut 31, 217–236 (2018). https://doi.org/10.1007/s13163-017-0237-2
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DOI: https://doi.org/10.1007/s13163-017-0237-2