The Pure Virtual Braid Group is Quadratic

If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra grK need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this thesis we give a sufficient criterion (called the PVH Criterion) for grK to be quadratic. When K is the group algebra of a group G, quadraticity is known to be equivalent to the existence of a (not necessarily homomorphic) universal finite type invariant for G. Thus the PVH Criterion also implies the existence of a universal finite type invariant for the group G. We apply the PVH Criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic, and hence that these groups have a universal finite type invariant.

Department dc:contributor.department

Mathematics

Year dc:date.issued

2012

Author dc:creator

• Lee, Peter

Advisor dc:contributor.advisor

• Bar-Natan, Dror

• Pure Virtual Braids
• Quadraticity
• Graded 1-Formal
• Universal Finite Type Invariant

Language dc:language.iso

en_ca

Handle dc:identifier.uri

http://hdl.handle.net/1807/32806

OAI identifier oai:identifier

oai:utoronto.scholaris.ca:1807/32806