Semi-Infinite Highest Weight Categories
Jonathan Brundan, Catharina Stroppel
Abstract
We develop axiomatics of highest weight categories and quasi-hereditary algebras in order to incorporate two semi-infinite situations which are in Ringel duality with each other; the underlying posets are either <italic>upper finite</italic> or <italic>lower finite</italic> . We also consider various more general sorts of stratified categories. In the upper finite cases, we give an alternative characterization of these categories in terms of based quasi-hereditary algebras and based stratified algebras, which are certain locally unital algebras possessing triangular bases.
Topics & Concepts
MathematicsUnitalPure mathematicsDuality (order theory)Order (exchange)Algebra over a fieldCombinatoricsFinanceEconomicsAlgebraic structures and combinatorial modelsAdvanced Topics in AlgebraAdvanced Algebra and Logic