Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584053 | Journal of Algebra | 2016 | 43 Pages |
Abstract
We analyze the BGG Category O over a large class of generalized Weyl algebras (henceforth termed GWAs). Given such a “triangular” GWA for which Category O decomposes into a direct sum of subcategories, we study in detail the homological properties of blocks with finitely many simples. As consequences, we show that the endomorphism algebra of a projective generator of such a block is quasi-hereditary, finite-dimensional, and graded Koszul. We also classify all tilting modules in the block, as well as all submodules of all projective and tilting modules. Finally, we present a novel connection between blocks of triangular GWAs and Young tableaux, which provides a combinatorial interpretation of morphisms and extensions between objects of the block.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Apoorva Khare, Akaki Tikaradze,