Consider J = Ext2(DB,B).
(B = BB is the left
regular representation, whereas DB is the dual of the right regular representation).
We consider the semi-direct extension C(B) of B by J.
This algebra C(B) is called the cluster tilted algebra corresponding to B.
These cluster tilted algebras have been introduced by Buan-Marsh-Reiten
(in a different, but equivalent way);
the description given here is due to Zhu and
Assem-Bruestle-Schiffler.