Results 41 to 50 of about 3,969 (116)
CAT(0) and cubulated Shephard groups
Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.Abstract Shephard groups are common generalizations of Coxeter groups, Artin groups, and graph products of cyclic groups. Their definition is similar to that of a Coxeter group, but generators may have arbitrary order rather than strictly order 2. We extend a well‐known result that Coxeter groups are CAT(0)$\mathrm{CAT}(0)$ to a class of Shephard ...
Katherine M. Goldman
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Representations of Braid Groups and Generalisations [PDF]
, 2007 We define and study extensions of Artin's representation and braid monodromy representation to the case of topological and algebraical generalisations of braid groups. In particular we provide faithful representations of braid groups of oriented surfaces
Bardakov, Valerij G., Bellingeri, Paolo
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Anti-trees and right-angled Artin subgroups of braid groups
, 2015 We prove that an arbitrary right-angled Artin group $G$ admits a quasi-isometric group embedding into a right-angled Artin group defined by the opposite graph of a tree.
Kim, Sang-hyun, Koberda, Thomas
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On representations of Artin–Tits and surface braid groups
Journal of Group Theory, 2011 AbstractWe define and study extensions of the Artin and Perron–Vannier representations of braid groups to topological and algebraic generalizations of braid groups. We provide faithful representations of braid groups of oriented surfaces with boundary as automorphisms of finitely generated free groups.
Bardakov, Valeriy G., Bellingeri, Paolo
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PBW Deformations of Smash Products Involving Hopf Algebra of Kac–Paljutkin Type
Journal of Mathematics, Volume 2025, Issue 1, 2025.Let H2n2 be the Kac–Paljutkin–type Hopf algebra of dimension 2n2, A its graded Koszul Artin–Schelter regular H2n2‐module algebra of Dimension 2, A! the Koszul dual of A, and Acop the braided‐opposite algebra of A. This paper describes (0, 1)‐degree PBW deformations of the smash product A♯H2n2 and those of A!♯H2n2 under the condition that the Koszul ...
Yujie Gao, Shilin Yang, Naihuan Jing
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Elementary equivalence in Artin groups of finite type
, 2018 Irreducible Artin groups of finite type can be parametrized via their associated Coxeter diagrams into six sporadic examples and four infinite families, each of which is further parametrized by the natural numbers.
Kabiraj, Arpan +2 more
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Link splitting deformation of colored Khovanov–Rozansky homology
Proceedings of the London Mathematical Society, Volume 129, Issue 3, September 2024.Abstract We introduce a multiparameter deformation of the triply‐graded Khovanov–Rozansky homology of links colored by one‐column Young diagrams, generalizing the “y$y$‐ified” link homology of Gorsky–Hogancamp and work of Cautis–Lauda–Sussan. For each link component, the natural set of deformation parameters corresponds to interpolation coordinates on ...
Matthew Hogancamp +2 more
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Shi arrangements and low elements in Coxeter groups
Proceedings of the London Mathematical Society, Volume 129, Issue 2, August 2024.Abstract Given an arbitrary Coxeter system (W,S)$(W,S)$ and a non‐negative integer m$m$, the m$m$‐Shi arrangement of (W,S)$(W,S)$ is a subarrangement of the Coxeter hyperplane arrangement of (W,S)$(W,S)$. The classical Shi arrangement (m=0$m=0$) was introduced in the case of affine Weyl groups by Shi to study Kazhdan–Lusztig cells for W$W$.
Matthew Dyer +3 more
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On the linearity of Artin braid groups
Journal of Algebra, 2003 The author proves that all Artin groups of crystallographic type have a faithful representation of dimension the number of reflections of the associated Coxeter group. The faithfulness criterion which is used is that of \textit{D. Krammer} [Ann. Math. (2) 155, No. 1, 131-156 (2002; Zbl 1020.20025)].
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Rational cross‐sections, bounded generation, and orders on groups
Journal of the London Mathematical Society, Volume 109, Issue 6, June 2024.Abstract We provide new examples of groups without rational cross‐sections (also called regular normal forms), using connections with bounded generation and rational orders on groups. Our examples contain a finitely presented HNN‐extension of the first Grigorchuk group. This last group is the first example of finitely presented group with solvable word
Corentin Bodart
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