A Categorical Structure for the Virtual Braid Group

Kauffman, LH; Lambropoulou, S

dc.contributor.author	Kauffman, LH	en
dc.contributor.author	Lambropoulou, S	en
dc.date.accessioned	2014-03-01T02:01:38Z
dc.date.available	2014-03-01T02:01:38Z
dc.date.issued	2011	en
dc.identifier.issn	00927872	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29216
dc.subject	Pure virtual braid group	en
dc.subject	Pure welded braid group	en
dc.subject	Virtual braid group	en
dc.subject	Welded braid group	en
dc.title	A Categorical Structure for the Virtual Braid Group	en
heal.type	journalArticle	en
heal.identifier.primary	10.1080/00927872.2011.617280	en
heal.identifier.secondary	http://dx.doi.org/10.1080/00927872.2011.617280	en
heal.publicationDate	2011	en
heal.abstract	This article gives a new interpretation of the virtual braid group in terms of a strict monoidal category SC that is freely generated by one object and three morphisms, two of the morphisms corresponding to basic pure virtual braids and one morphism corresponding to a transposition in the symmetric group. This point of view makes many relationships between the virtual braid group and the pure virtual braid group apparent, and makes representations of the virtual braid groups and pure virtual braid groups via solutions to the algebraic Yang-Baxter Equation equally transparent. In this categorical framework, the virtual braid group has nothing to do with the plane and nothing to do with virtual crossings. It is a natural group associated with the structure of algebraic braiding. © 2011 Copyright Taylor and Francis Group, LLC.	en
heal.journalName	Communications in Algebra	en
dc.identifier.doi	10.1080/00927872.2011.617280	en
dc.identifier.volume	39	en
dc.identifier.issue	12	en
dc.identifier.spage	4679	en
dc.identifier.epage	4704	en