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Supersolvability an...
Supersolvability and the Koszul property of root ideal arrangements
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- Hultman, Axel (author)
- Linköpings universitet,Matematik och tillämpad matematik,Tekniska fakulteten
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(creator_code:org_t)
- American Mathematical Society (AMS), 2016
- 2016
- English.
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In: Proceedings of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9939 .- 1088-6826. ; 144, s. 1401-1413
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Abstract
Subject headings
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- A root ideal arrangement A_I is the set of reflecting hyperplanes corresponding to the roots in an order ideal I of the root poset on the positive roots of a finite crystallographic root system. A characterisation of supersolvable root ideal arrangements is obtained. Namely, A_I is supersolvable if and only if I is chain peelable, meaning that it is possible to reach the empty poset from I by in each step removing a maximal chain which is also an order filter. In particular, supersolvability is preserved under taking subideals. We identify the maximal ideals that correspond to non-supersolvable arrangements. There are essentially two such ideals, one in type D_4 and one in type F_4. By showing that A_I is not line-closed if I contains one of these, we deduce that the Orlik-Solomon algebra OS(A_I) has the Koszul property if and only if A_I is supersolvable.
Subject headings
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
Keyword
- hyperplane arrangement
- root poset
- supersolvability
- Koszul algebra
Publication and Content Type
- ref (subject category)
- art (subject category)
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