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{{Short description|Generalized Braid group on the Sphere}} ...tion |last=Ihara |first=Yasutaka |title=Automorphisms of Pure Sphere Braid Groups and Galois Representations |date=2007 |url=https://doi.org/10.1007/978-0-81 ...

[[File:Alexander closure of a braid.svg|350px|thumb|Braid closure]] ...e '''Markov theorem''' gives necessary and sufficient conditions for two [[braid (mathematics)|braids]] to have closures that are equivalent [[knot (mathema ...

...s | title=Gaussian groups and Garside groups, two generalisations of Artin groups | journal=[[Proceedings of the London Mathematical Society]] | volume=79 | ...citation | last=Garside | first=Frank A. | title=The braid group and other groups | journal=Quarterly Journal of Mathematics |series=Second Series | volume=2 ...

{{Short description|Braid group representation}} ...er representation''' is a [[group representation|representation]] of the [[braid group]]s. It fits into a family of representations called the Lawrence rep ...

...-access = free }}</ref> Dehornoy's original discovery of the order on the braid group used [[huge cardinal]]s, but there are now several more elementary co .../math> strings. Define a <math>\sigma_i</math>'''-positive word''' to be a braid that admits at least one expression in the elements <math>\sigma_1, \ldots, ...

...rems asserting that the [[group cohomology|group homology]] of a series of groups <math>G_1 \subset G_2 \subset \cdots </math> is stable, i.e., ...llen|first= D.|author-link=Daniel Quillen|chapter=Finite generation of the groups ''K''_''i'' of rings of algebraic integers.|title=Algebraic K-the ...

...ant relationship exists between the quantum Yang-Baxter equation and the [[braid equation]]. If <math>R</math> satisfies the quantum Yang-Baxter equation, t ..., V.G. (1991). "Invariants of 3-manifolds via link polynomials and quantum groups". ''[[Inventiones Mathematicae]]''. 103: 547–597.</ref> ...

...normal forms. It is often discussed specifically in application of [[braid groups]], which notably are infinite (and the group elements can take variable qua ...ubstantial research has been done on attacks to the conjugacy problem on [[braid group]]s, although no full efficient solution has achieved. ...

...au representation''' is a [[group representation|representation]] of the [[braid group]]s, named after and originally studied by the German mathematician We Consider the [[braid group]] {{math|''B_n''}} to be the [[mapping class group]] of a d ...

...lied to the tensor diagram and thus they present a representation of the [[braid group]]. [[Category:Quantum groups]] ...

...protocols. Later several other non-commutative structures like [[Thompson groups]], [[polycyclic group]]s, [[Grigorchuk group]]s, and [[matrix group]]s hav ==Platform groups== ...

# (Braid relations) *The Artin [[braid group]] embeds in the BMW algebra: <math>B_n \hookrightarrow \mathrm{C}_n</ ...

...fied spaces has uses everywhere from pure mathematics topics such as braid groups and [[Lawrence–Krammer representation|representations]] to robot motion pla ...

...space of the <math>n</math>th [[braid group]] (see [[#Connection to braid groups|below]]). == Connection to braid groups == ...

...bolic subgroups essentially coincide in the case of finite real reflection groups. Parabolic subgroups arise in the theory of [[algebraic group]]s, through == Background: reflection groups == ...

...ochon |first=Carlos |date=2003-02-28 |title=Anyons from nonsolvable finite groups are sufficient for universal quantum computation |url=https://journals.aps. ...

...e realization of 25 of the 26 [[Sporadic group|sporadic groups]] as Galois groups over <math>\Q</math> — the only remaining sporadic group left to realize be ...ox |first1=R. |last2=Neuwirth |first2=L. |date=1962-06-01 |title=The Braid Groups. |journal=Mathematica Scandinavica |url=http://www.mscand.dk/article/view/1 ...

...ass group of surfaces are related to various other groups, in particular [[braid group]]s and [[outer automorphism group]]s. === The mapping class groups of the sphere and the torus === ...

...problems]] from combinatorial group theory, namely the [[word problem for groups|word problem]], [[conjugacy problem]] and [[membership problem]], are linea ...ugacy [[search problem]]s are in ''GenP'' for all fixed finitely presented groups.<ref>A. Ushakov, ''Dissertation'', City University of New York, 2005.</ref> ...

...s, polytopes, braid groups, cyclic homology, geometry of orbits of compact groups, ...Groups'' by Claudio Procesi|url=https://www.maa.org/press/maa-reviews/lie-groups-an-approach-through-invariants-and-representations|website=MAA Reviews, Mat ...