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• W3102257961 startingPage "461" @default.
• W3102257961 abstract "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 paper 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 such 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 (not necessarily homomorphic) universal finite type invariant." @default.
• W3102257961 created "2020-11-23" @default.
• W3102257961 creator A5022585138 @default.
• W3102257961 date "2012-10-09" @default.
• W3102257961 modified "2023-10-18" @default.
• W3102257961 title "The pure virtual braid group is quadratic" @default.
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• W3102257961 doi "https://doi.org/10.1007/s00029-012-0107-1" @default.
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