The virtual and universal braids

• Autorzy: Valerij G. Bardakov
• Języki publikacji: EN

Abstrakty

EN

We study the structure of the virtual braid group. It is shown that the virtual braid group is a semi-direct product of the virtual pure braid group and the symmetric group. Also, it is shown that the virtual pure braid group is a semi-direct product of free groups. From these results we obtain a normal form of words in the virtual braid group. We introduce the concept of a universal braid group. This group contains the classical braid group and has as quotients the singular braid group, virtual braid group, welded braid group, and classical braid group.

Kategorie tematyczne

• 20F05: Generators, relations, and presentations
• 20F10: Word problems, other decision problems, connections with logic and automata
• 20F36: Braid groups; Artin groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 184
• Numer: 1
• Strony: 1-18

Daty

wydano

2004

Twórcy

autor

Valerij G. Bardakov

• Sobolev Institute of Mathematics, Novosibirsk 630090, Russia

Identyfikatory

DOI

10.4064/fm184-0-1