On the vertices of indecomposable modules over dihedral 2-groups

On the Vertices of Indecomposable Modules over Dihedral 2-groups

Let k be an algebraically closed field of characteristic 2. We calculate the vertices of all indecomposable kD8-modules for the dihedral group D8 of order 8. We also give a conjectural formula of the induced module of a string module from kT0 to kG where G is a dihedral group G of order ≥ 8 and where T0 is a dihedral subgroup of index 2 of G. Some cases where we verified this formula are given.

On the Tensor Products of Modules for Dihedral 2-Groups

The only groups for which all indecomposable modules are ‘knowable’ are those with cyclic, dihedral, semidihedral, and quaternion Sylow p-subgroups. The structure of the Green ring for groups with cyclic and V4 Sylow p-subgroups are known, but no others have been determined. Of the remaining groups, the dihedral 2-groups have the simplest module category but yet the tensor products of any two i...

On Indecomposable Modules over the Virasoro Algebra

It is proved that an indecomposable Harish-Chandra module over the Virasoro algebra must be (i) a uniformly bounded module, or (ii) a module in Category O, or (iii) a module in Category O, or (iv) a module which contains the trivial module as one of its composition factors.

A Group of Order 8 That’s Hard: Indecomposable String Modules for Dihedral Groups

Endotrivial Modules over Groups with Quaternion or Semi-dihedral Sylow 2-subgroup

Suppose that G is a finite group and that k is a field of characteristic p. Endotrivial kG-modules appear in a natural way in many areas surrounding local analysis of finite groups. They were introduced by Dade [14] who classified them in the case that G is an abelian p-group. A complete classification of endotrivial modules over the modular group rings of p-groups was completed just a few year...