dorsal/arxiv
View SchemaOn Hopf algebras and the elimination theorem for free Lie algebras
| Authors | J. Lepowsky, R. L. Wilson |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9505022 |
| URL | https://arxiv.org/abs/q-alg/9505022 |
Abstract
The elimination theorem for free Lie algebras, a general principle which describes the structure of a free Lie algebra in terms of free Lie subalgebras, has been recently used by E. Jurisich to prove that R. Borcherds' ``Monster Lie algebra'' has certain large free Lie subalgebras, illuminating part of Borcherds' proof that the moonshine module vertex operator algebra obeys the Conway-Norton conjectures. In the present expository note, we explain how the elimination theorem has a very simple and natural generalization to, and formulation in terms of, Hopf algebras. This fact already follows from general results contained in unpublished 1972 work, unknown to us when we wrote this note, of R. Block and P. Leroux.
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"abstract": "The elimination theorem for free Lie algebras, a general principle which\ndescribes the structure of a free Lie algebra in terms of free Lie subalgebras,\nhas been recently used by E. Jurisich to prove that R. Borcherds\u0027 ``Monster Lie\nalgebra\u0027\u0027 has certain large free Lie subalgebras, illuminating part of\nBorcherds\u0027 proof that the moonshine module vertex operator algebra obeys the\nConway-Norton conjectures. In the present expository note, we explain how the\nelimination theorem has a very simple and natural generalization to, and\nformulation in terms of, Hopf algebras. This fact already follows from general\nresults contained in unpublished 1972 work, unknown to us when we wrote this\nnote, of R. Block and P. Leroux.",
"arxiv_id": "q-alg/9505022",
"authors": [
"J. Lepowsky",
"R. L. Wilson"
],
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"q-alg",
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"title": "On Hopf algebras and the elimination theorem for free Lie algebras",
"url": "https://arxiv.org/abs/q-alg/9505022"
},
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