1996/01/18 by Penkava, Michael
#FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.q-alg/9601018
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.