dorsal/arxiv
View SchemaInfinity Algebras and the Homology of Graph Complexes
| Authors | Michael Penkava |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9601018 |
| URL | https://arxiv.org/abs/q-alg/9601018 |
Abstract
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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"abstract": "An A-infinity algebra is a generalization of a associative algebra, and an\nL-infinity algebra is a generalization of a Lie algebra. In this paper, we show\nthat an L-infinity algebra with an invariant inner product determines a cycle\nin the homology of the complex of metric ordinary graphs. Since the cyclic\ncohomology of a Lie algebra with an invariant inner product determines\ninfinitesimal deformations of the Lie algebra into an L-infinity algebra with\nan invariant inner product, this construction shows that a cyclic cocycle of a\nLie algebra determines a cycle in the homology of the graph complex. In this\npaper a simple proof of the corresponding result for A-infinity algebras, which\nwas proved in a different manner in an earlier paper, is given.",
"arxiv_id": "q-alg/9601018",
"authors": [
"Michael Penkava"
],
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"q-alg",
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"title": "Infinity Algebras and the Homology of Graph Complexes",
"url": "https://arxiv.org/abs/q-alg/9601018"
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