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.Comment: 20 page

Chamberlin, Samuel H.

English

arXiv

Samuel Chamberlin

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Integral Bases for the Universal Enveloping Algebras of Map Algebras

Given a finite-dimensional, simple Lie algebra g overC and A, a commutative, associative algebra with unityover C, we exhibit a Z-form for the universalenveloping algebra of the map algebra for g and anexplicit Z-basis for this Z-form. We also produceexplicit commutation formulas in the universal envelopingalgebra of the map algebra of sl2 that allow us to write certainelements in Poincaré-Birkhoff-Witt order.Finally we give some applications of these formulas to therepresentation theory of the map algebras for sl2

Chamberlin, Samuel Herron

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Integral Bases for the Universal Enveloping Algebras of Map Algebras

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