Integral Bases for the Universal Enveloping Algebras of Map Algebras.

摘要

Given a finite-dimensional, simple Lie algebra g over C and A, a commutative, associative algebra with unity over C , we exhibit an integral form for the universal enveloping algebra of the map algebra, g ⊗ A, and an explicit Z -basis for this integral form. We also produce explicit commutation formulas in the universal enveloping algebra of sl2 ⊗ A that allow us to write certain elements in Poincare-Birkhoff-Witt order.;Finally we give some applications of these formulas to the representation theory of the map algebras for sl2 .