On representations of twisted group rings
نویسنده
چکیده
We generalize certain parts of the theory of group rings to the twisted case. Let G be a finite group acting (possibly trivially) on a field L of characteristic coprime to the order of the kernel of this operation. Let K ⊆ L be the fixed field of this operation, let S be a discrete valuation ring with field of fractions K, maximal ideal generated by π and integral closure T in L. We compute the colength of T ≀G in a maximal order in L≀G. Moreover, if S/πS is finite, we compute the S/πS-dimension of the center of T ≀ G/Jac(T ≀ G). If this quotient is split semisimple, this yields a formula for the number of simple T ≀G-modules, generalizing Brauer’s formula.
منابع مشابه
Twisted Group Rings of Metacyclic Groups
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