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Lorentzian Lattices and E-Polytopes

Title
Lorentzian Lattices and E-Polytopes
Authors
Clingher, AdrianLee, Jae-Hyouk
Ewha Authors
이재혁
SCOPUS Author ID
이재혁scopus
Issue Date
2018
Journal Title
SYMMETRY-BASEL
ISSN
2073-8994JCR Link
Citation
SYMMETRY-BASEL vol. 10, no. 10
Keywords
lorentzian latticeweyl grouproot latticedual latticelinesgosset polytopeE-polytope
Publisher
MDPI
Indexed
SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
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).
DOI
10.3390/sym10100443
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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