Lorentzian Lattices and E-Polytopes
- 주제(키워드) lorentzian lattice , weyl group , root lattice , dual lattice , lines , gosset polytope , E-polytope
- 주제(기타) Multidisciplinary Sciences
- 설명문(일반) [Clingher, Adrian] Univ Missouri, Dept Math & Comp Sci, St Louis, MO 63121 USA; [Lee, Jae-Hyouk] Ewha Womans Univ, Dept Math, 52 Ewhayeodae Gil, Seoul 03760, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 MDPI
- 발행년도 2018
- URI http://www.dcollection.net/handler/ewha/000000156496
- 본문언어 영어
- Published As http://dx.doi.org/10.3390/sym10100443
초록/요약
We consider certain En-type root lattices embedded within the standard Lorentzian lattice Z(n+1) (3 <= n <= 8) and study their discrete geometry from the point of view of del Pezzo surface geometry. The lattice Z(n+1) decomposes as a disjoint union of affine hyperplanes which satisfy a certain periodicity. We introduce the notions of line vectors, rational conic vectors, and rational cubics vectors and their relations to E-polytopes. We also discuss the relation between these special vectors and the combinatorics of the Gosset polytopes of type (n-4)(21).
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