# ## About: Quasitriangular Hopf algebraGotoSponge NotDistinct Permalink

An Entity of Type : yago:Science105999797, within Data Space : dbpedia-live.openlinksw.com associated with source document(s)  In mathematics, a Hopf algebra, H, is quasitriangular if there exists an invertible element, R, of such that * for all , where is the coproduct on H, and the linear map is given by , * , * , where , , and , where , , and , are algebra morphisms determined by R is called the R-matrix. It is possible to construct a quasitriangular Hopf algebra from a Hopf algebra and its dual, using the Drinfeld quantum double construction. If the Hopf algebra H is quasitriangular, then the category of modules over H is braided with braiding .

AttributesValues
rdf:type
sameAs
foaf:isPrimaryTopicOf
rdfs:comment
• In mathematics, a Hopf algebra, H, is quasitriangular if there exists an invertible element, R, of such that * for all , where is the coproduct on H, and the linear map is given by , * , * , where , , and , where , , and , are algebra morphisms determined by R is called the R-matrix. It is possible to construct a quasitriangular Hopf algebra from a Hopf algebra and its dual, using the Drinfeld quantum double construction. If the Hopf algebra H is quasitriangular, then the category of modules over H is braided with braiding .
rdfs:label
• Quasitriangular Hopf algebra
has abstract
• In mathematics, a Hopf algebra, H, is quasitriangular if there exists an invertible element, R, of such that * for all , where is the coproduct on H, and the linear map is given by , * , * , where , , and , where , , and , are algebra morphisms determined by R is called the R-matrix. As a consequence of the properties of quasitriangularity, the R-matrix, R, is a solution of the Yang-Baxter equation (and so a module V of H can be used to determine quasi-invariants of braids, knots and links). Also as a consequence of the properties of quasitriangularity, ; moreover , , and . One may further show that theantipode S must be a linear isomorphism, and thus S2 is an automorphism. In fact, S2 is given by conjugating by an invertible element: where (cf. Ribbon Hopf algebras). It is possible to construct a quasitriangular Hopf algebra from a Hopf algebra and its dual, using the Drinfeld quantum double construction. If the Hopf algebra H is quasitriangular, then the category of modules over H is braided with braiding .
Link to the Wikipage edit URL
extraction datetime
Link to the Wikipage history URL
Wikipage page ID
page length (characters) of wiki page
Wikipage modification datetime
Wiki page out degree
Wikipage revision ID
Link to the Wikipage revision URL
dbp:wikiPageUsesTemplate
dct:subject
is foaf:primaryTopic of
is Wikipage redirect of
Faceted Search & Find service v1.17_git39 as of Aug 10 2019   OpenLink Virtuoso version 08.03.3319 as of Sep 1 2020, on Linux (x86_64-generic-linux-glibc25), Single-Server Edition (61 GB total memory)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2021 OpenLink Software