On Hopf algebras and the elimination theorem for free Lie algebras

Details On Hopf algebras and the elimination theorem for free Lie algebras On Hopf algebras and the elimination theorem for free Lie algebras

1995-05-18

arxiv.org/abs/q-alg/9505022v1

Mathematics

Quantum Algebra

LaTeX file. 13 pages. To appear in ``Moonshine, the Monster and Related Topics,'' Proc. Joint Summer Research Conference, Moun

Scientific paper

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 This fact already follows from general results contained in unpublished 1972 work, unknown to us when we wrote this note, of R. Block and P. Leroux.

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