Integral Bases for the Universal Enveloping Algebras of Map Algebras
- Author(s): Chamberlin, Samuel Herron
- Advisor(s): Chari, Vyjayanthi
- et al.
Given a finite-dimensional, simple Lie algebra g over
C and A, a commutative, associative algebra with unity
over C, we exhibit a Z-form for the universal
enveloping algebra of the map algebra for g and an
explicit Z-basis for this Z-form. We also produce
explicit commutation formulas in the universal enveloping
algebra of the map algebra of sl2 that allow us to write certain
elements in Poincaré-Birkhoff-Witt order.
Finally we give some applications of these formulas to the
representation theory of the map algebras for sl2.