Results 31 to 40 of about 104 (85)

Intersection of parabolic subgroups in Euclidean braid groups: a short proof

Comptes Rendus. Mathématique
We give a short proof for the fact, already proven by Thomas Haettel, that the arbitrary intersection of parabolic subgroups in Euclidean Braid groups $A[\tilde{A}_n]$ is again a parabolic subgroup. To that end, we use that the spherical-type Artin group
Cumplido, María, Gavazzi, Federica, Paris, Luis   +2 more
doaj   +1 more source

Some Aspects of Mathematical and Physical Approaches for Topological Quantum Computation [PDF]

Computer Science Journal of Moldova, 2011
A paradigm to build a quantum computer, based on topological invariants is highlighted. The identities in the ensemble of knots, links and braids originally discovered in relation to topological quantum field theory are shown: how they define Artin ...
V. Kantser
doaj  

Membership problems in braid groups and Artin groups [PDF]

Journal of the London Mathematical Society
Abstract We study several natural decision problems in braid groups and Artin groups. We classify the Artin groups with decidable submonoid membership problem in terms of the nonexistence of certain forbidden‐induced subgraphs of the defining graph.
Gray, Robert D., Nyberg-Brodda, Carl-Fredrik   +1 more
openaire   +2 more sources

Braided finite automata and representation theory

Nuclear Physics B
We introduce classical and non-deterministic finite automata associated with representations of the braid group. After briefly reviewing basic definitions on finite automata, Coxeter’s groups and the associated word problem, we turn to the Artin ...
Anastasia Doikou
doaj   +1 more source

ON ARTIN'S BRAID GROUP AND POLYCONVEXITY IN THE CALCULUS OF VARIATIONS [PDF]

Journal of the London Mathematical Society, 2003
Summary: Let \(\Omega \subset \mathbb{R}^2\) be a bounded Lipschitz domain and let \(F: \Omega \times \mathbb{R}_+^{2\times 2}\to \mathbb{R}\) be a Carathéodory integrand such that \(F(x,\cdot)\) is polyconvex for \({\mathcal L}^2\)-a.e. \(x\in \Omega\).
openaire   +2 more sources

Presentations of the braid group of the complex reflection group G(d,d,n)$G(d,d,n)$

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract We show that the braid group associated to the complex reflection group G(d,d,n)$G(d,d,n)$ is an index d$d$ subgroup of the braid group of the orbifold quotient of the complex numbers by a cyclic group of order d$d$. We also give a compatible presentation of G(d,d,n)$G(d,d,n)$ and its braid group for each tagged triangulation of the disk with ...
Francesca Fedele, Bethany Rose Marsh
wiley   +1 more source

Skein theory for the Links–Gould polynomial

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract Building further on work of Marin and Wagner, we give a cubic braid‐type skein theory of the Links–Gould polynomial invariant of oriented links and prove that it can be used to evaluate any oriented link, adding this polynomial to the list of polynomial invariants that can be computed by skein theory. As a consequence, we prove that this skein
Stavros Garoufalidis, Matthew Harper, Rinat Kashaev, Ben‐Michael Kohli, Jiebo Song, Guillaume Tahar   +5 more
wiley   +1 more source

Combination theorems for Wise's power alternative

Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.
Abstract We show that Wise's power alternative is stable under certain group constructions, use this to prove the power alternative for new classes of groups and recover known results from a unified perspective. For groups acting on trees, we introduce a dynamical condition that allows us to deduce the power alternative for the group from the power ...
Mark Hagen, Alexandre Martin, Giovanni Sartori   +2 more
wiley   +1 more source

Structure theorems for braided Hopf algebras

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract We develop versions of the Poincaré–Birkhoff–Witt and Cartier–Milnor–Moore theorems in the setting of braided Hopf algebras. To do so, we introduce new analogs of a Lie algebra in the setting of a braided monoidal category, using the notion of a braided operad.
Craig Westerland
wiley   +1 more source

Homogeneous braids are visually prime

Journal of Topology, Volume 18, Issue 3, September 2025.
Abstract We show that closures of homogeneous braids are visually prime, addressing a question of Cromwell. The key technical tool for the proof is the following criterion concerning primeness of open books, which we consider to be of independent interest.
Peter Feller, Lukas Lewark, Miguel Orbegozo Rodriguez   +2 more
wiley   +1 more source