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- Braided_vector_space abstract "In mathematics, a braided vectorspace is a vector space together with an additional structure map symbolizing interchanging of two vector tensor copies:such that the Yang–Baxter equation is fulfilled. Hence drawing tensor diagrams with an overcrossing the corresponding composed morphism is unchanged when a Reidemeister move is applied to the tensor diagram and thus they present a representation of the braid group.As first example, every vector space is braided via the trivial braiding (simply flipping). A superspace has a braiding with negative sign in braiding two odd vectors. More generally, a diagonal braiding means that for a -base we haveA good source for braided vector spaces entire braided monoidal categories with braidings between any objects , most importantly the modules over quasitriangular Hopf algebras and Yetter–Drinfeld modules over finite groups (such as above)If additionally possesses an algebra structure inside the braided category ("braided algebra") one has a braided commutator (e.g. for a superspace the anticommutator): Examples of such braided algebras (and even Hopf algbebras) are the Nichols algebras, that are by definition generated by a given braided vectorspace. They appear as quantum Borel part of quantum groups and often (e.g. when finite or over an abelian group) possess an arithmetic root system, multiple Dynkin diagrams and a PBW-basis made up of braided commutators just like the ones in semisimple Lie algebras.".
- Braided_vector_space wikiPageID "32518704".
- Braided_vector_space wikiPageRevisionID "599214565".
- Braided_vector_space hasPhotoCollection Braided_vector_space.
- Braided_vector_space subject Category:Hopf_algebras.
- Braided_vector_space subject Category:Quantum_groups.
- Braided_vector_space type Abstraction100002137.
- Braided_vector_space type Algebra106012726.
- Braided_vector_space type Cognition100023271.
- Braided_vector_space type Content105809192.
- Braided_vector_space type Discipline105996646.
- Braided_vector_space type Group100031264.
- Braided_vector_space type HopfAlgebras.
- Braided_vector_space type KnowledgeDomain105999266.
- Braided_vector_space type Mathematics106000644.
- Braided_vector_space type PsychologicalFeature100023100.
- Braided_vector_space type PureMathematics106003682.
- Braided_vector_space type QuantumGroups.
- Braided_vector_space type Science105999797.
- Braided_vector_space comment "In mathematics, a braided vectorspace is a vector space together with an additional structure map symbolizing interchanging of two vector tensor copies:such that the Yang–Baxter equation is fulfilled.".
- Braided_vector_space label "Braided vector space".
- Braided_vector_space sameAs m.0h1hldb.
- Braided_vector_space sameAs Q4955657.
- Braided_vector_space sameAs Q4955657.
- Braided_vector_space sameAs Braided_vector_space.
- Braided_vector_space wasDerivedFrom Braided_vector_space?oldid=599214565.
- Braided_vector_space isPrimaryTopicOf Braided_vector_space.