## Departmental PHD Thesis Exam – Peter Lee

Everyone welcome.  Refreshments will be served in the Math Lounge before the exam.

Monday, November 7, 2011, 1-2 p.m., in BA 6183

PhD Candidate:  Stephen Peter Lee

If an augmented algebra $K$ over ${\mathbb Q}$ is filtered by powers of  its augmentation ideal $I$, the associated graded algebra $gr_I K$ need not in general be quadratic: although it is generated in degree $1$, its relations may not be generated by homogeneous relations of degree $2$.  We give a criterion which is equivalent to $gr_I K$ being quadratic. We apply this 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.