EVENT DETAILS AND ABSTRACT

Title: Structure theorems for braided Hopf algebras
Speaker: Craig Westerland
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Abstract:

The Poincaré-Birkhoff-Witt and Milnor-Moore theorems are fundamental tools for understanding the structure of Hopf algebras. Part of the classification of pointed Hopf algebras involves a notion of ``braided Hopf algebras.” I will present work in progress which will establish analogues of the Poincaré-Birkhoff-Witt and Milnor-Moore theorems in this setting. The main new tool is a notion of a braided Lie algebra defined in terms of braided operads. This can be used to establish forms of these results, and also presents an unexpected connection to profinite braid groups and related operads.