Integral Bases for the Universal Enveloping Algebras of Map Algebras

Details Integral Bases for the Universal Enveloping Algebras of Map Algebras Integral Bases for the Universal Enveloping Algebras of Map Algebras

2011-07-06

arxiv.org/abs/1107.1249v2

Mathematics

Representation Theory

20 pages

Scientific paper

Given a finite-dimensional, complex simple Lie algebra we exhibit an integral
form for the universal enveloping algebra of its map algebra, and an explicit
integral basis for this integral form. We also produce explicit commutation
formulas in the universal enveloping algebras of the map algebras of sl_2 that
allow us to write certain elements in Poincare-Birkhoff-Witt order.

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