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- Title
A category O for oriented matroids.
- Authors
Kowalenko, Ethan; Mautner, Carl
- Abstract
We associate to a sufficiently generic oriented matroid program and choice of linear system of parameters a finite-dimensional algebra, whose representation theory is analogous to blocks of Bernstein--Gelfand--Gelfand category O. When the data above comes from a generic linear program for a hyperplane arrangement, we recover the algebra defined by Braden--Licata-- Proudfoot--Webster. Applying our construction to non-linear oriented matroid programs provides a large new class of algebras. For Euclidean oriented matroid programs, the resulting algebras are quasihereditary and Koszul, as in the linear setting. In the non-Euclidean case, we obtain algebras that are not quasi-hereditary and not known to be Koszul, but still have a natural class of standard modules and satisfy numerical analogues of quasi-heredity and Koszulity on the level of graded Grothendieck groups.
- Subjects
MATROIDS; GROTHENDIECK groups; ALGEBRA; NON-Euclidean geometry; NUMERICAL analysis
- Publication
Journal of Combinatorial Algebra, 2023, Vol 7, Issue 1, p159
- ISSN
2415-6302
- Publication type
Article
- DOI
10.4171/JCA/71