DUALITY FOR PARTIAL GROUP ACTIONS

Christian LOMP

Makale detayları

DUALITY FOR PARTIAL GROUP ACTIONS

Yazarlar:

Christian LOMP

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2008 Vol.4 Issue 4, pp.53-62

Belge Tipi:

Makale

Yayın Tarihi:

11/2008

Belge Dili:

Türkçe

Document ID (Org No.):

2000718419

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

Özet:

 

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 Mn(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 ∗α G) #k[G]∗ of the partial skew group ring A ∗α G and k[G]∗ is isomorphic to a direct product of the form K × eMn(A)e where e is a certain idempotent of Mn(A) and K is a subalgebra of (A ∗α G) #k[G]∗. Moreover A ∗α G is shown to be isomorphic to a separable subalgebra of eMn(A)e. We also look at duality for infinite partial group actions.

Makale detayları

DUALITY FOR PARTIAL GROUP ACTIONS

Yazarlar: Christian LOMP

Yayıncı: Abdullah HARMANCI

Dergi: International Electronic Journal of Algebra 2008 Vol.4 Issue 4, pp.53-62

Belge Tipi: Makale

Yayın Tarihi: 11/2008

Belge Dili: Türkçe

Document ID (Org No.): 2000718419

Sıklık: Aylık

eISSN: 1306-6048

pISSN: 1306-6048

Sayı

Yazarlar:

Christian LOMP

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2008 Vol.4 Issue 4, pp.53-62

Belge Tipi:

Makale

Yayın Tarihi:

11/2008

Belge Dili:

Türkçe

Document ID (Org No.):

2000718419

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048