Duality for partial group actions
| dc.creator | Lomp, Christian | |
| dc.date | 2007-11-06 | |
| dc.date.accessioned | 2026-07-07T08:40:59Z | |
| dc.date.available | 2026-07-07T08:40:59Z | |
| dc.description | 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 G-stable ideals of A. The ring A*G is G-graded, i.e.G coacts on A*G. The Cohen-Montgomery 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 Cohen-Montgomery duality carries over to partial group actions in the sense of R.Exel. In particular we show that the smash product (A*_αG)#k[G]^* of the partial skew group ring A*_αG 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 *_αG)#k[G]^*. Moreover A*_αG 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. | |
| dc.identifier | https://arxiv.org/abs/0711.0849 | |
| dc.identifier | http://arxiv.org/abs/0711.0849 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141539 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Operator Algebras | |
| dc.title | Duality for partial group actions | |
| dc.type | text |