dorsal/arxiv
View SchemaMoonshine Cohomology
| Authors | Bong H. Lian, Gregg J. Zuckerman |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9501015 |
| URL | https://arxiv.org/abs/q-alg/9501015 |
Abstract
We construct a new cohomology functor from the a certain category of {\it quantum operator algebras} to the category of {\it Batalin-Vilkovisky algebras}. This {\it Moonshine cohomology} has, as a group of natural automorphisms, the Fischer-Griess Monster finite group. We prove a general vanishing theorem for this cohomology. For a certain commutative QOA attached to a rank two hyperbolic lattice, we show that the degree one cohomology is isomorphic to the so-called Lie algebra of physical states. In the case of a rank two unimodular lattice, the degree one cohomology gives a new construction of Borcherd's Monster Lie algebra. As applications, we compute the graded dimensions and signatures of this cohomology as a hermitean Lie algebra graded by a hyperbolic lattice. In the first half of this paper, we give as preparations an exposition of the theory of quantum operator algebras. Some of the results here were announced in lectures given by the first author at the Research Institute for Mathematical Sciences in Kyoto in September 94.
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"abstract": "We construct a new cohomology functor from the a certain category of {\\it\nquantum operator algebras} to the category of {\\it Batalin-Vilkovisky\nalgebras}. This {\\it Moonshine cohomology} has, as a group of natural\nautomorphisms, the Fischer-Griess Monster finite group. We prove a general\nvanishing theorem for this cohomology. For a certain commutative QOA attached\nto a rank two hyperbolic lattice, we show that the degree one cohomology is\nisomorphic to the so-called Lie algebra of physical states. In the case of a\nrank two unimodular lattice, the degree one cohomology gives a new construction\nof Borcherd\u0027s Monster Lie algebra. As applications, we compute the graded\ndimensions and signatures of this cohomology as a hermitean Lie algebra graded\nby a hyperbolic lattice. In the first half of this paper, we give as\npreparations an exposition of the theory of quantum operator algebras. Some of\nthe results here were announced in lectures given by the first author at the\nResearch Institute for Mathematical Sciences in Kyoto in September 94.",
"arxiv_id": "q-alg/9501015",
"authors": [
"Bong H. Lian",
"Gregg J. Zuckerman"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"title": "Moonshine Cohomology",
"url": "https://arxiv.org/abs/q-alg/9501015"
},
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