Derived bracket construction and anti-cyclic subcomplex of Leibniz (co)homology complex
Quantum Algebra
2013-12-30 v1
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.
Keywords
Cite
@article{arxiv.1312.7268,
title = {Derived bracket construction and anti-cyclic subcomplex of Leibniz (co)homology complex},
author = {K. Uchino},
journal= {arXiv preprint arXiv:1312.7268},
year = {2013}
}
Comments
21 pages