On collapsing racks

F. FANTINO

Córdoba

Workshop; Quantum day; 2013

FaMAF-UNC

In the context of the Lifting method, an important step in the classification of finite-dimensional complex pointed Hopf algebras is the determination of all finite-dimensional Nichols algebras of Yetter- Drinfeld modules over groups. This leads to the study of finite-dimensional Nichols algebras of braided vector spaces arising from pairs (X, q), where X is a rack and q a 2-cocycle. We said that a rack X collapses if the Nichols algebra associated to (X,q) has infinite dimension for any cocycle q. In this lecture, we will talk about some criteria to determine when a rack collapses.