TY - JOUR
T1 - Semisimple algebras, Galois actions and group cohomology
AU - Aljadeff, Eli
AU - Robinson, Derek J.S.
PY - 1994/6/3
Y1 - 1994/6/3
N2 - Let K be any field of characteristic p>0 and let G be a finite group acting on K via a map τ. The skew group algebra KτG may be non-semisimple (precisely when p∥H|, H = Kerτ). We provide necessary conditions for the existence of a class αε{lunate}H2(G, K*) which "twists" the skew group algebra K>τG into a semisimple crossed product KατG. Further, we give a thorough analysis of the converse problem namely whether these conditions are also sufficient for the existence of a "semisimple 2-cocycle". As a consequence we show this it is indeed so in many cases, in particular whenever G is a p-group.
AB - Let K be any field of characteristic p>0 and let G be a finite group acting on K via a map τ. The skew group algebra KτG may be non-semisimple (precisely when p∥H|, H = Kerτ). We provide necessary conditions for the existence of a class αε{lunate}H2(G, K*) which "twists" the skew group algebra K>τG into a semisimple crossed product KατG. Further, we give a thorough analysis of the converse problem namely whether these conditions are also sufficient for the existence of a "semisimple 2-cocycle". As a consequence we show this it is indeed so in many cases, in particular whenever G is a p-group.
UR - http://www.scopus.com/inward/record.url?scp=38149146239&partnerID=8YFLogxK
U2 - 10.1016/0022-4049(94)90002-7
DO - 10.1016/0022-4049(94)90002-7
M3 - 文章
AN - SCOPUS:38149146239
SN - 0022-4049
VL - 94
SP - 1
EP - 15
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 1
ER -