Results 21 to 30 of about 3,993 (104)
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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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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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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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
wiley +1 more source
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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The paraunitary group of a von Neumann algebra
Bulletin of the London Mathematical Society, Volume 54, Issue 4, Page 1220-1231, August 2022., 2022 Abstract It is proved that the pure paraunitary group over a von Neumann algebra coincides with the structure group of its projection lattice. The structure group of an arbitrary orthomodular lattice (OML) is a group with a right invariant lattice order, and as such it is known to be a complete invariant of the OML.
Carsten Dietzel, Wolfgang Rump
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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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One-dimensional actions of Higman's group
Discrete Analysis, 2019 One-dimensional actions of Higman's group, Discrete Analysis 2019:20, 15 pp. In 1951 Higman constructed the first known example of an infinite finitely generated simple group. He began with the group $H$ that has presentation $\langle a,b,c,d|aba^{-1}=b^
Cristobal Rivas, Michele Triestino
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Braid groups and Artin groups [PDF]
, 2009 This article is a survey on the braid groups, the Artin groups, and the Garside groups. It is a presentation, accessible to non-experts, of various topological and algebraic aspects of these groups. It is also a report on three points of the theory: the faithful linear representations, the cohomology, and the geometrical representations.
openaire +2 more sources