Combinatorics of regular \(A_{2}\)-crystals
type: Item
instance of: scholarly article
title: Combinatorics of regular \(A_{2}\)-crystals
zbMATH Open document ID: 1158.17004
author: Vladimir I. Danilov
author: G. A. Koshevoy
author: Alexander V. Karzanov
published in: Journal of Algebra
publication date: 2007-04-18T00:00:00Z
review text: The authors study regular \(2\)-colored simply laced crystals for the Cartan matrix of type \(A_2\), which are connected and in which all monochromatic paths are finite. The main structural result of the paper says that each such crystal can be produced using replicating and gluing together in a certain way, from two crystals of a very special form. As a consequence, the combinatorial structure of such crystals becomes rather transparent and the authors obtain several corollaries on combinatorial, polyhedral and other properties of such crystals. In particular, it turns out that such crystal is a Hasse diagram of a finite lattice. A structural characterization of some other class of crystals is also given.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 05E15
zbMATH DE Number: 5144390
zbMATH Keywords: crystal
zbMATH Keywords: simply laced algebra
zbMATH Keywords: graph
zbMATH Keywords: coloring
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2006.11.035
OpenAlex ID: W1986557165
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DOI: 10.1016/J.JALGEBRA.2006.11.035
description: scientific article; zbMATH DE number 5144390