Infinity Algebras and the Homology of Graph Complexes

Details Infinity Algebras and the Homology of Graph Complexes Infinity Algebras and the Homology of Graph Complexes

1996-01-18

arxiv.org/abs/q-alg/9601018v1

Mathematics

Quantum Algebra

14 pages, amslatex document, 4 figures

Scientific paper

An A-infinity algebra is a generalization of a associative algebra, and an L-infinity algebra is a generalization of a Lie algebra. In this paper, we show that an L-infinity algebra with an invariant inner product determines a cycle in the homology of the complex of metric ordinary graphs. Since the cyclic cohomology of a Lie algebra with an invariant inner product determines infinitesimal deformations of the Lie algebra into an L-infinity algebra with an invariant inner product, this construction shows that a cyclic cocycle of a Lie algebra determines a cycle in the homology of the graph complex. In this paper a simple proof of the corresponding result for A-infinity algebras, which was proved in a different manner in an earlier paper, is given.

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