Results 21 to 30 of about 5,399,954 (113)
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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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
Braid pictures for Artin groups [PDF]
Transactions of the American Mathematical Society, 2002 We define the braid groups of a two-dimensional orbifold and introduce conventions for drawing braid pictures. We use these to realize the Artin groups associated to the spherical Coxeter diagrams A_n, B_n=C_n and D_n and the affine diagrams tilde{A}_n, tilde{B}_n, tilde{C}_n and tilde{D}_n as subgroups of the braid groups of various simple orbifolds ...
openaire +3 more sources
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
wiley +1 more source
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
wiley +1 more source
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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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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MARKOV AND ARTIN NORMAL FORM THEOREM FOR BRAID GROUPS [PDF]
International Journal of Algebra and Computation, 2007 In this paper we will present the results of Artin–Markov on braid groups by using the Gröbner–Shirshov basis. As a consequence we can reobtain the normal form of Artin–Markov–Ivanovsky as an easy corollary.
Leonid A. Bokut +2 more
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The Tits alternative for non-spherical Pride groups [PDF]
, 2008 Pride groups, or 'groups given by presentations in which each defining relator involves at most two types of generators', include Coxeter groups, Artin groups, triangles of groups, and Vinberg's groups defined by periodic paired relations.
Williams, Gerald +5 more
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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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