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arXiv · 1312.7268

Derived bracket construction and anti-cyclic subcomplex of Leibniz (co)homology complex

K. Uchino
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Abstract

An arbitrary Leibniz algebra can be embedded in a differential graded Lie algebra via the derived bracket construction. Such an embedding is called a derived bracket representation. We will construct the universal version of the derived bracket representation, prove that the principal part of the target dg Lie algebra defines a subcomplex of Leibniz (co)homology complex and that the existence of the subcomplex is a reflection of the anti-cyclicity of the Leibniz operad.

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K. Uchino. 2013-12-27. Derived bracket construction and anti-cyclic subcomplex of Leibniz (co)homology complex. https://arxiv.org/abs/1312.7268

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