Koszulness and supersolvability for Dirichlet arrangements
Copyright policy )Koszulness and supersolvability for Dirichlet arrangements
We prove that the cone over a Dirichlet arrangement is supersolvable if and only if its Orlik-Solomon algebra is Koszul. This was previously shown for four other classes of arrangements. We exhibit an infinite family of cones over Dirichlet arrangements that are combinatorially distinct from these other four classes.
- University of Michigan–Flint United States
- University of Michigan Ann Arbor United States
- University of Michigan–Ann Arbor United States
- Regents of the University of Michigan - Ann Arbor United States
Quadratic and Koszul algebras, Orlik-Solomon algebras, Koszul algebras, Combinatorial aspects of matroids and geometric lattices, supersolvable, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Dirichlet arrangements, hyperplane arrangements, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 52C35 (Primary) 05B35, 16S37 (Secondary)
Quadratic and Koszul algebras, Orlik-Solomon algebras, Koszul algebras, Combinatorial aspects of matroids and geometric lattices, supersolvable, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Dirichlet arrangements, hyperplane arrangements, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 52C35 (Primary) 05B35, 16S37 (Secondary)
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