Deformation of a projection in the multipleir algebra and projection lifting from the corona algebra of a non-simple C*-algebra

2013/05/22 by Hyun Ho Lee, Lee, Hyun Ho
Mathematics · #46L35 #55P10 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1305.5006

openalex publication_date 2013/05/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let X be a unit interval or a unit circle and let B be a σ_p-unital, purely infinite, simple C\sp*-algebra such that its multiplier algebra M(B) has real rank zero. Then we determine necessary and sufficient conditions for a projection in the corona algebra of C(X)⊗ B to be liftable to a projection in the multiplier algebra. This generalizes a result proved by L. Brown and the author \citeBL. The main technical tools are divided into two parts. The first part is borrowed from the author's previous paper(JFA 260 (2011)). The second part is a proposition showing that we can produce a sub-projection, with an arbitrary rank which is prescribed as K-theoretical data, of a projection or a co-projection in the multiplier algebra of C(X)⊗ B under a suitable "infinite rank and co-rank" condition.

Related

• Homotopy classification of projections in the corona algebra of a non-simple C\sp *-algebra
• Purely infinite corona algebras
• Strict comparison of projections and positive combinations of projections in certain multiplier algebras
• Real rank of some multiplier algebras
• C*-algebra generated by projections