DUALITY FOR PARTIAL GROUP ACTIONS

Volume: 4 Number: 4 December 1, 2008
  • Christian Lomp
EN

DUALITY FOR PARTIAL GROUP ACTIONS

Abstract

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.

Keywords

Details

Primary Language

English

Subjects

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Journal Section

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Authors

Christian Lomp This is me

Publication Date

December 1, 2008

Submission Date

December 1, 2008

Acceptance Date

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Published in Issue

Year 2008 Volume: 4 Number: 4

APA
Lomp, C. (2008). DUALITY FOR PARTIAL GROUP ACTIONS. International Electronic Journal of Algebra, 4(4), 53-62. https://izlik.org/JA98MY35AT
AMA
1.Lomp C. DUALITY FOR PARTIAL GROUP ACTIONS. IEJA. 2008;4(4):53-62. https://izlik.org/JA98MY35AT
Chicago
Lomp, Christian. 2008. “DUALITY FOR PARTIAL GROUP ACTIONS”. International Electronic Journal of Algebra 4 (4): 53-62. https://izlik.org/JA98MY35AT.
EndNote
Lomp C (December 1, 2008) DUALITY FOR PARTIAL GROUP ACTIONS. International Electronic Journal of Algebra 4 4 53–62.
IEEE
[1]C. Lomp, “DUALITY FOR PARTIAL GROUP ACTIONS”, IEJA, vol. 4, no. 4, pp. 53–62, Dec. 2008, [Online]. Available: https://izlik.org/JA98MY35AT
ISNAD
Lomp, Christian. “DUALITY FOR PARTIAL GROUP ACTIONS”. International Electronic Journal of Algebra 4/4 (December 1, 2008): 53-62. https://izlik.org/JA98MY35AT.
JAMA
1.Lomp C. DUALITY FOR PARTIAL GROUP ACTIONS. IEJA. 2008;4:53–62.
MLA
Lomp, Christian. “DUALITY FOR PARTIAL GROUP ACTIONS”. International Electronic Journal of Algebra, vol. 4, no. 4, Dec. 2008, pp. 53-62, https://izlik.org/JA98MY35AT.
Vancouver
1.Christian Lomp. DUALITY FOR PARTIAL GROUP ACTIONS. IEJA [Internet]. 2008 Dec. 1;4(4):53-62. Available from: https://izlik.org/JA98MY35AT