A Koszul category of representations of finitary Lie algebras

By Elizabeth Dan-Cohen, I. Penkov, Vera Serganova. 2011

58 citations recorded by the source corpus.

Abstract We find for each simple finitary Lie algebra g a category T g of integrable modules in which the tensor product of copies of the natural and conatural modules is injective. The objects in T g can be defined as the finite length absolute weight modules, where by absolute weight module we mean a module which is a weight module for every splitting Cartan subalgebra of g . The category T g is Koszul in the sense that it is antiequivalent to the category of locally unitary finite-dimensional modules over a certain direct limit of finite-dimensional Koszul algebras. We describe these finite-dimensional algebras explicitly. We also prove an equivalence of the categories T o ( ∞ ) and T sp ( ∞ ) corresponding respectively to the orthogonal and symplectic finitary Lie algebras o ( ∞ ) , sp ( ∞ ) .

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/10d1d8c3a55dcdb295813cace746683c049c587f