Nongraded Infinite-Dimensional Simple Lie Algebras

Details Nongraded Infinite-Dimensional Simple Lie Algebras Nongraded Infinite-Dimensional Simple Lie Algebras

2000-11-30

arxiv.org/abs/math/0011264v1

Mathematics

Quantum Algebra

18 pages

Scientific paper

Nongraded infinite-dimensional Lie algebras appeared naturally in the theory of Hamiltonian operators, the theory of vertex algebras and their multi-variable analogues. They play important roles in mathematical physics. This survey article is written based on the author's seminar talks on nongraded infinite-dimensional simple Lie algebras. The key constructional ingredients of our Lie algebras are locally-finite derivations. The structure spaces of some families of these simple Lie algebras can be viewed as analogues of vector bundles with Lie algebras as fibers. We also believe that some of our simple Lie algebras could be related to noncommutative geometry.

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