turkmath.org

Recently, Boltje and Carman described a ring of so-called "coherent character tuples" which is isomorphic to the trivial source ring of a finite group. I will explain refinements of Boltje and Carman's result that describe the Grothendieck group of the category of trivial source modules belonging to a fixed p-block of a finite group. These refinements are used to introduce a new type of block equivalence which we call a "strong isotypy." A splendid Rickard equivalence or a p-permutation equivalence induces a strong isotypy, and a strong isotypy restricts to an isotypy in the sense of Broué.