Virgilius-Aurelian Minuţă
Babeş-Bolyai University, Cluj-Napoca, Romania

We introduce a notion of group graded Picent group associated to a strongly group graded algebra, and we establish an exact sequence linking this group and the Picent group of the 1-component. This sequence is a version of the Beattie - del Río sequence from 1996. Furthermore, we show that there is an interesting connection between these two exact sequences, which involves the 5-term exact sequence. One motivation for these results comes from our proof that there is a link between character triples and a special type of group graded Morita equivalences. These algebra equivalences are obtained via group graded bimodules which satisfy some additional conditions involving how the elements of the bimodule interact with the centralizer subalgebra of the aforementioned algebras. Classes of isomorphisms of such bimodules form the graded Picent group, which is a subgroup of the graded Picard group. This is a joint work with Andrei Marcus.