Lifting properties of blocks
Lange, Corinna; Nebe, Gabriele Charlotte (Thesis advisor); Plesken, Wilhelm (Thesis advisor)
Aachen (2016, 2017)
Dissertation / PhD Thesis
Dissertation, RWTH Aachen University, 2016
We consider blocks of group algebras of finite groups over a complete discrete valuation ring R with the goal of giving an explicit description of the basic algebra of the block. In the cases we study, we use the structure of the corresponding algebra over the residue field in positive characteristic and construct lifts of that algebra. We also impose certain rational conditions fulfilled by the block over R on the lift. Subsequently we show that the constructed lift is the unique lift fulfilling those conditions and thereby know that it is isomorphic to the basic algebra. We apply this method to blocks of semidihedral defect and to defect 3 blocks of symmetric groups.