2017/11/30 by Thanasin Nampaisarn, Nampaisarn, Thanasin
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.1711.11234
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. We study the category O consisting of all \mathfrakh-weight \mathfrakg-modules which are locally \mathfrakb-finite and have finite-dimensional \mathfrakh-weight spaces. The focus is on very special Borel subalgebras called the Dynkin Borel subalgebras. This paper serves as an initial passage to the understanding of categories O for infinite-dimensional root-reductive Lie algebras.