The Center of Thin Gaussian Groups

By Matthieu Picantin. 2001

51 citations recorded by the source corpus.

Abstract Thin Gaussian groups are a natural generalization of spherical Artin groups, namely groups of fractions of monoids in which the existence of least common multiples is kept as an hypothesis, but the relations between the generators are not supposed to necessarily be of Coxeter type. Here we completely describe the center of thin Gaussian groups by constructing a minimal generating set for the quasi-center. We deduce that every thin Gaussian group is an iterated crossed product of thin Gaussian groups with a cyclic center.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/72cf9334d10e291a98f6084006301a62ea7f60f3

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In Computational Theory and Mathematics

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2. David Peifer

In Discrete Mathematics and Combinatorics

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In Geometry and Topology

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Citations in the corpus

• The group of parenthesized braids (2004, unknown): “(For general Zappa-Szép products, see [7]—or [29] where the name “‘crossed product” is used.”
• The K(π,1)-conjecture for the affine braid groups (2003, methodology): “have been studied extensively by Dehornoy, Picantin, and others ([D1], [D2], [DP], [ P1 ]).”
• Garside Groups and Yang–Baxter Equation (2009, unknown): “Let xi xj be in X, then from [16], either xi = xj or the left gcd of xi and xj is .”