THE COMPOSITION SERIES OF IDEALS OF THE PARTIAL-ISOMETRIC CROSSED PRODUCT BY SEMIGROUP OF ENDOMORPHISMS

- Journal title : Journal of the Korean Mathematical Society
- Volume 52, Issue 4, 2015, pp.869-889
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2015.52.4.869

Title & Authors

THE COMPOSITION SERIES OF IDEALS OF THE PARTIAL-ISOMETRIC CROSSED PRODUCT BY SEMIGROUP OF ENDOMORPHISMS

ADJI, SRIWULAN; ZAHMATKESH, SAEID;

ADJI, SRIWULAN; ZAHMATKESH, SAEID;

Abstract

Let be the positive cone in a totally ordered abelian group , and an action of by extendible endomorphisms of a -algebra A. Suppose I is an extendible -invariant ideal of A. We prove that the partial-isometric crossed product embeds naturally as an ideal of , such that the quotient is the partial-isometric crossed product of the quotient algebra. We claim that this ideal together with the kernel of a natural homomorphism gives a composition series of ideals of studied by Lindiarni and Raeburn.

Keywords

-algebra;endomorphism;semigroup;partial isometry;crossed product;primitive ideal;hull-kernel closure;

Language

English

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