# Craig Westerland (University of Minnesota)

January 20, 2022 at Northeastern (virtual)

Title: Braids and Hopf algebras

Abstract: The Milnor–Moore theorem identifies a large class of Hopf algebras as enveloping algebras of the Lie algebras of their primitives. If we broaden our definition of a Hopf algebra to that of a braided Hopf algebra, much of this structure theory falls apart. The most obvious reason is that the primitives in a braided Hopf algebra no longer form a Lie algebra. In this talk, we will discuss recent work to understand what precisely is the algebraic structure of the primitives in a braided Hopf algebra in order to “repair” the Milnor–Moore theorem in this setting. It turns out that this structure is closely related to the dualizing module for the braid groups, which implements dualities in the (co)homology of the braid groups.

The colloquium meets (by default) on Thursdays at 4:30 PM Eastern in varying modalities (contact institutional organizers for details). The organizers include Bong Lian at Brandeis; Fabian Gundlach, Myrto Mavraki, and Assaf Shani at Harvard; Scott Sheffield at MIT; and Matthew Hogancamp, Ben Knudsen, Gabor Lippner, and Jonathan Weitsman at Northeastern. This website is maintained by Ben Knudsen. The image of Boston is the property of Wikimedia user King of Hearts and is reproduced here under Creative Commons license CC BY-SA 4.0. Images of speakers are their own property and are reproduced here with permission.