Abstract
We shall show that the Hecke order HDn of the dihedral group of order 2·pn over Z[q,q−1] for an odd prime p is a projectively cellular order. We describe the corresponding cell ideals and compute the extension groups between the corresponding cell modules; some are Z-torsion-free, some are Fp[q,q−1]-torsion-free. Moreover, we show that HDn is a Brauer tree order to the tree •——∘——• with central exceptional vertex of multiplicity pn−1·(p−1)/2.
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