Results 1 to 10 of about 53 (53)
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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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
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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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Associahedra for finite‐type cluster algebras and minimal relations between g‐vectors
Proceedings of the London Mathematical Society, Volume 127, Issue 3, Page 513-588, September 2023., 2023 Abstract We show that the mesh mutations are the minimal relations among the g${\bm{g}}$‐vectors with respect to any initial seed in any finite‐type cluster algebra. We then use this algebraic result to derive geometric properties of the g${\bm{g}}$‐vector fan: we show that the space of all its polytopal realizations is a simplicial cone, and we then ...
Arnau Padrol +3 more
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Semisimple four‐dimensional topological field theories cannot detect exotic smooth structure
Journal of Topology, Volume 16, Issue 2, Page 542-566, June 2023., 2023 Abstract We prove that semisimple four‐dimensional oriented topological field theories lead to stable diffeomorphism invariants and can therefore not distinguish homeomorphic closed oriented smooth four‐manifolds and homotopy equivalent simply connected closed oriented smooth four‐manifolds.
David Reutter
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Proceedings of the London Mathematical Society, Volume 125, Issue 6, Page 1332-1352, December 2022., 2022 Abstract We generalize the construction of Rouquier complexes to the setting of one‐sided singular Soergel bimodules. Singular Rouquier complexes are defined by taking minimal complexes of restricted Rouquier complexes. We show that they retain many of the properties of ordinary Rouquier complexes: they are Δ$\Delta$‐split, they satisfy a vanishing ...
Leonardo Patimo
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Homological stability for Iwahori–Hecke algebras
Journal of Topology, Volume 15, Issue 4, Page 2174-2215, December 2022., 2022 Abstract We show that the Iwahori–Hecke algebras Hn$\mathcal {H}_n$ of type An−1$A_{n-1}$ satisfy homological stability, where homology is interpreted as an appropriate Tor group. Our result precisely recovers Nakaoka's homological stability result for the symmetric groups in the case that the defining parameter is equal to 1.
Richard Hepworth
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A polynomial algorithm for the braid double shielded public key cryptosystems
Қарағанды университетінің хабаршысы. Математика сериясы, 2016 We propose new provable practical deterministic polynomial time algorithm of cryptographic analysis for the braid Wang, Xu, Li, Lin and Wang «Double shielded public key cryptosystems», where the authors recommended the Artin braid groups Bn as platforms
V.A. Roman’kov
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