Semi-Infinite Highest Weight Categories

By Jonathan Brundan, C. Stroppel. Memoirs of the American Mathematical Society, 2018

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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 upper finite or lower finite. 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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

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