Results 11 to 20 of about 104 (85)
Gröbner–Shirshov basis for the braid group in the Artin–Garside generators
Journal of Symbolic Computation, 2008 In this paper, we give a Groebner-Shirshov basis of the braid group $B_{n+1}$ in the Artin--Garside generators. As results, we obtain a new algorithm for getting the Garside normal form, and a new proof that the braid semigroup $B^+{n+1}$ is the subsemigroup in $B_{n+1}$.
L A Bokut
exaly +4 more sources
New developments in the theory of Artin's braid groups
Topology and Its Applications, 2003 The author reviews some recent developments in the theory of the Artin braid groups. In particular, he sketches the three different proofs of Dehornoy's theorem, which states that the Artin braid groups are right-orderable [see \textit{P. Dehornoy}, Trans. Am. Math. Soc. 345, No. 1, 115-150 (1994; Zbl 0837.20048)].
Dale Rolfsen
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A GATHERING PROCESS IN ARTIN BRAID GROUPS [PDF]
International Journal of Algebra and Computation, 2006 In this paper we construct a gathering process by the means of which we obtain new normal forms in braid groups. The new normal forms generalize Artin–Markoff normal forms and possess an extremely natural geometric description. In the two last sections of the paper we discuss the implementation of the introduced gathering process and the questions ...
Evgeinj S. Esyp, Ilya V. Kazachkov
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The $$R_\infty $$ property for pure Artin braid groups [PDF]
Monatshefte für Mathematik, 2021 In this paper we prove that all pure Artin braid groups $P_n$ ($n\geq 3$) have the $R_\infty$ property. In order to obtain this result, we analyse the naturally induced morphism $\operatorname{\text{Aut}}(P_n) \to \operatorname{\text{Aut}}(Γ_2 (P_n)/Γ_3(P_n))$ which turns out to factor through a representation $ρ\colon S_{n+1} \to \operatorname{\text ...
Karel Dekimpe +2 more
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Higher Braid Groups and Regular Semigroups from Polyadic-Binary Correspondence
Mathematics, 2021 In this note, we first consider a ternary matrix group related to the von Neumann regular semigroups and to the Artin braid group (in an algebraic way).
Steven Duplij
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Curve graphs for Artin–Tits groups of type B, A∼ and C∼ are hyperbolic
Transactions of the London Mathematical Society, 2021 The graph of irreducible parabolic subgroups is a combinatorial object associated to an Artin–Tits group A defined so as to coincide with the curve graph of the (n+1)‐times punctured disk when A is Artin's braid group on (n+1) strands.
Matthieu Calvez +1 more
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Graph braid groups and right-angled Artin groups [PDF]
Transactions of the American Mathematical Society, 2011 We give a necessary and sufficient condition for a graph to have a right-angled Artin group as its braid group for braid index ≥
Kim, JH Kim, Jee-Hyoun +2 more
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Tensor stable moduli stacks and refined representations of quivers
Journal of the London Mathematical Society, Volume 108, Issue 6, Page 2085-2114, December 2023., 2023 Abstract In this paper, we look at the problem of modular realisations of derived equivalences, and more generally, the problem of recovering a Deligne–Mumford stack X$\mathbb {X}$ and a bundle T$\mathcal {T}$ on it, via some moduli problem (on X$\mathbb {X}$ or A=EndXT$A = \operatorname{End}_{\mathbb {X}} \mathcal {T}$). The key issue is, how does one
Tarig Abdelgadir, Daniel Chan
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Interval groups related to finite Coxeter groups Part II
Transactions of the London Mathematical Society, Volume 10, Issue 1, Page 100-123, December 2023., 2023 Abstract We provide a complete description of the presentations of the interval groups related to quasi‐Coxeter elements in finite Coxeter groups. In the simply laced cases, we show that each interval group is the quotient of the Artin group associated with the corresponding Carter diagram by the normal closure of a set of twisted cycle commutators ...
Barbara Baumeister +3 more
wiley +1 more source
Topological model of composite fermions in the cyclotron band generator picture: New insights
Results in Physics, 2018 A combinatorial group theory in the braid groups is correlated with the unusual “anyon” statistic of particles in 2D Hall system in the fractional quantum regime well.
Beata Staśkiewicz
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