Laura Nastasescu 

Our initial aim was to answer the question: does the Frobenius(symmetric) property transfers from a strongly graded algebra to its homogenous component of trivial degree? 

Related to it, we investigate invertible bimodules and the Picard group of a finite dimensional quasi-Frobenius algebra R. 

We compute the Picard group, the automorphism group and the group of outer automorphisms of a 9-dimensional quasi-Frobenius algebra, which is not Frobenius, constructed by Nakayama. 

Using these results and a semitrivial extension construction, we give an example of a symmetric strongly graded algebra whose trivial homogenous component is not even Frobenius. 

This is joint work with Sorin Dascalescu and Constantin Nastasescu