Thi Hoa Nguyen

The global dimension is an important homological invariant of an algebra, often serving as a good analogue of the dimension of a smooth affine algebraic variety.

 However, there are examples where the global dimension does not align with geometric intuition. 

This often leads to consider the Hochschild cohomological dimension rather than the global dimension. 

It is thus a natural question to determine classes of algebras for which the global dimension and the Hochschild cohomological dimension coincide, and this is a well-known fact when our algebra is graded connected or is a Hopf algebra.

In this talk, I will discuss some properties of braided Hopf algebras and explain a result which states that equality between global and Hochshild dimensions still holds for a braided Hopf algebra in the category of comodules over a cosemisimple coquasitriangular Hopf algebra. 

The presentation will cover results from a recent paper with my supervisor Julien Bichon.