About: Racks and quandles

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In mathematics, racks and quandles are sets with binary operations satisfying axioms analogous to the Reidemeister moves used to manipulate knot diagrams. While mainly used to obtain invariants of knots, they can be viewed as algebraic constructions in their own right. In particular, the definition of a quandle axiomatizes the properties of conjugation in a group.

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rdf:type	train
rdfs:label	Rack (jednotka) (cs) Quandle (de) Rak dan ganjalan (in) 圭 (数学) (ja) Racks and quandles (en)
rdfs:comment	Rack je měřítko výkonu textilních strojů. 1 rack znamená * u osnovních pletacích strojů = 480 řádků pleteniny.Používá se zejména při výpočtu spotřeby příze. * na bobinetech: - u strojů na výrobu záclonoviny = 240 obrátek stroje - na strojích k výrobě hladkého tylu = 720 obrátek stroje - na strojích k výrobě krajky = 960 obrátek stroje. Používá se hlavně k posouzení jakosti výrobků. Např. jakostní krajky se vyrábějí rychlostí 35-50 cm /rack, nejlevnější až 200 cm/rack. (cs) Ein Quandle ist in der Mathematik eine algebraische Struktur, die vor allem in der Knotentheorie Anwendung findet. (de) In mathematics, racks and quandles are sets with binary operations satisfying axioms analogous to the Reidemeister moves used to manipulate knot diagrams. While mainly used to obtain invariants of knots, they can be viewed as algebraic constructions in their own right. In particular, the definition of a quandle axiomatizes the properties of conjugation in a group. (en) Dalam matematika, rak dan ganjalan adalah himpunan dengan aksioma pemuas operasi biner dimana analog dengan yang digunakan untuk memanipulasi diagram . Meskipun sebagian besar digunakan untuk mendapatkan invarian simpul, hal tersebut dipandang sebagai konstruksi aljabar dengan hak sendiri. Secara khusus, definisi dari sebuah ganjalan melakukan aksioma pada properti dari dalam group. (in) 数学における圭（けい）、分配亜群（ぶんぱいあぐん、дистрибутивныи Группоид; distributive groupoid, quandle; カンドル）および残滓（ざんし、rack; ラック)は、結び目の局所変形であるライデマイスター移動を図式操作と考えたときに抽出される公理と類似の公理を満たす二項演算を備えた集合である。主に結び目理論を背景として研究されるものであるが、抽象代数学的な構造としては、自身の右からの作用を備えた代数系であると見なすことができる。 (ja)
dcterms:subject	Non-associative algebra Knot theory
Wikipage page ID	1140981 (xsd:integer)
Wikipage revision ID	1110121967 (xsd:integer)
Link from a Wikipage to another Wikipage	Alissa Crans University of Cambridge Reidemeister move Mathematics Wirtinger presentation Fundamental group Automorphism Non-associative algebra Three-dimensional space Distributive property Laurent polynomial Laver table Alexander polynomial Euclidean space Knot group Knot theory Reflection (mathematics) Riemannian symmetric space Knot theory Group (mathematics) Isomorphic Abstract algebra John Horton Conway Binary operation Biracks and biquandles Cohomology Egbert Brieskorn Homeomorphism Groupoids Inner automorphism Finite geometry Knot diagram Orientation reversing Tame knot Colin Rourke dbr:Roger_Fenn dbr:David_E._Joyce_(mathematician) dbr:Gavin_Wraith dbr:Set(mathematics)
Link from a Wikipage to an external page	http://www.ams.org/samplings/feature-column/fc-2016-03 https://arxiv.org/abs/1002.4429 https://arxiv.org/abs/math/0211096 https://arxiv.org/abs/math/0409602v1 https://ncatlab.org/nlab/show/quandle
sameAs	Racks and quandles Racks and quandles Racks and quandles Racks and quandles Racks and quandles Racks and quandles Racks and quandles
dbp:wikiPageUsesTemplate	dbt:Algebraic_structures dbt:Anchor dbt:Short_description dbt:Visible_anchor
has abstract	Rack je měřítko výkonu textilních strojů. 1 rack znamená * u osnovních pletacích strojů = 480 řádků pleteniny.Používá se zejména při výpočtu spotřeby příze. * na bobinetech: - u strojů na výrobu záclonoviny = 240 obrátek stroje - na strojích k výrobě hladkého tylu = 720 obrátek stroje - na strojích k výrobě krajky = 960 obrátek stroje. Používá se hlavně k posouzení jakosti výrobků. Např. jakostní krajky se vyrábějí rychlostí 35-50 cm /rack, nejlevnější až 200 cm/rack. (cs) Ein Quandle ist in der Mathematik eine algebraische Struktur, die vor allem in der Knotentheorie Anwendung findet. (de) In mathematics, racks and quandles are sets with binary operations satisfying axioms analogous to the Reidemeister moves used to manipulate knot diagrams. While mainly used to obtain invariants of knots, they can be viewed as algebraic constructions in their own right. In particular, the definition of a quandle axiomatizes the properties of conjugation in a group. (en) Dalam matematika, rak dan ganjalan adalah himpunan dengan aksioma pemuas operasi biner dimana analog dengan yang digunakan untuk memanipulasi diagram . Meskipun sebagian besar digunakan untuk mendapatkan invarian simpul, hal tersebut dipandang sebagai konstruksi aljabar dengan hak sendiri. Secara khusus, definisi dari sebuah ganjalan melakukan aksioma pada properti dari dalam group. (in) 数学における圭（けい）、分配亜群（ぶんぱいあぐん、дистрибутивныи Группоид; distributive groupoid, quandle; カンドル）および残滓（ざんし、rack; ラック)は、結び目の局所変形であるライデマイスター移動を図式操作と考えたときに抽出される公理と類似の公理を満たす二項演算を備えた集合である。主に結び目理論を背景として研究されるものであるが、抽象代数学的な構造としては、自身の右からの作用を備えた代数系であると見なすことができる。 (ja)
gold:hypernym	Sets
prov:wasDerivedFrom	wikipedia-en:Racks_and_quandles?oldid=1110121967&ns=0
page length (characters) of wiki page	11211 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Racks_and_quandles
is Link from a Wikipage to another Wikipage of	Quandle Quandles List of knot theory topics Quantum algebra Fundamental quandle Fundamental quandles Laver table Alexander quandle Alexander quandles Fox n-coloring Rack Involutory quandle Involutory quandles Biracks and biquandles Wrack (mathematics) Self-distributive Self-distributive law Self-distributive property Quandle (knot theory) Quandles and racks Rack (knot theory)

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