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Let Г + be the positive cone in a totally ordered abelian group Γ, and α an action of Г+ by extendible endomorphisms of a C∗-algebra A. Suppose I is an extendible α-invariant ideal of A. We prove that the partial-isometric crossed product I := I ×piso α Г+ embeds naturally as an ideal of A× piso α Г+, such that the quotient is the partial-isometric crossed product of the quotient algebra. We claim that this ideal I together with the kernel of a natural homomorphism Ø : A× piso α + → A × piso α Г+ gives a composition series of ideals of A ×piso α Г+ studied by Lindiarni and Raeburn.
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참고문헌 (9)
참고문헌 신청
B. K. Kwa´sniewski / 2013 / Crossed products by endomorphisms and reduction of relations in relative Cuntz-Pimsner algebras / J. Funct. Anal 264 (8) : 1806 ~ 1847
G. J. Murphy / 1987 / Ordered groups and Toeplitz algebras / J. Operator Theory 18 (2) : 303 ~ 326
I. Raeburn / 1998 / Morita Equivalence and Continuous-Trace C?-Algebras / Mathematical Surveys and Monographs 60
J. Lindiarni / 2004 / Partial-isometric crossed products by semigroups of endo-morphisms / J. Operator Theory 52 (1) : 61 ~ 87
N. J. Fowler / 2003 / Representations of Cuntz-Pimsner Algebras / Indiana Univ. Math. J 52 (3) : 569 ~ 605
G. J. Murphy / 1987 / Ordered groups and Toeplitz algebras / J. Operator Theory 18 (2) : 303 ~ 326
I. Raeburn / 1998 / Morita Equivalence and Continuous-Trace C?-Algebras / Mathematical Surveys and Monographs 60
J. Lindiarni / 2004 / Partial-isometric crossed products by semigroups of endo-morphisms / J. Operator Theory 52 (1) : 61 ~ 87
N. J. Fowler / 2003 / Representations of Cuntz-Pimsner Algebras / Indiana Univ. Math. J 52 (3) : 569 ~ 605
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