2020/12/02 by Thanasin Nampaisarn, Nampaisarn, Thanasin
Mathematics · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2012.01003
This is the second paper of a series of papers on a version of categories O for root-reductive Lie algebras. Let \mathfrakg be a root-reductive Lie algebra over an algebraically closed field \mathbbK of characteristic 0 with a splitting Borel subalgebra \mathfrakb containing a splitting maximal toral subalgebra \mathfrakh. For some pairs of blocks O[λ] and O[μ], the subcategories whose objects have finite length are equivalence via functors obtained by the direct limits of translation functors. Tilting objects can also be defined in O. There are also universal tilting objects D(λ) in parallel to the finite-dimensional cases.