
Mathematics 2007
Duality for partial group actionsAbstract: Given a finite group G acting as automorphisms on a ring A, the skew group ring A*G is an important tool for studying the structure of Gstable ideals of A. The ring A*G is Ggraded, i.e.G coacts on A*G. The CohenMontgomery duality says that the smash product A*G#k[G]^* of A*G with the dual group ring k[G]^* is isomorphic to the full matrix ring M_n(A) over A, where n is the order of G. In this note we show how much of the CohenMontgomery duality carries over to partial group actions in the sense of R.Exel. In particular we show that the smash product (A*_\alpha G)#k[G]^* of the partial skew group ring A*_\alpha G and k[G]^* is isomorphic to a direct product of the form K x eM_n(A)e where e is a certain idempotent of M_n(A) and K is a subalgebra of (A *_\alpha G)#k[G]^*. Moreover A*_\alpha G is shown to be isomorphic to a separable subalgebra of eM_n(A)e. We also look at duality for infinite partial group actions and for partial Hopf actions.
