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2013•Journal für die reine und angewandte Mathematik (Crelles Journal)Open access

On a notion of exactness for reduced free products of C*-algebras

Paul Skoufranis

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Abstract

Abstract We will study some modifications to the notion of an exact C*-algebra by replacing the minimal tensor product with the reduced free product. First we will demonstrate how the reduced free product of a short exact sequence of C*-algebras with another C*-algebra may be taken. It will then be demonstrated that this operation preserves exact sequences. We will also establish that adjoining arbitrary k-tuples of operators in a free way behaves well with respect to taking ultrapowers.

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Abstract We will study some modifications to the notion of an exact C*-algebra by replacing the minimal tensor product with the reduced free product. First we will demonstrate how the reduced free product of a short exact sequence of C*-algebras with another C*-algebra may be taken. It will then be demonstrated that this operation preserves exact sequences. We will also establish that adjoining arbitrary k-tuples of operators in a free way behaves well with respect to taking ultrapowers.

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Available abstract

Abstract We will study some modifications to the notion of an exact C*-algebra by replacing the minimal tensor product with the reduced free product. First we will demonstrate how the reduced free product of a short exact sequence of C*-algebras with another C*-algebra may be taken. It will then be demonstrated that this operation preserves exact sequences. We will also establish that adjoining arbitrary k-tuples of operators in a free way behaves well with respect to taking ultrapowers.

Key concepts: Tensor product, Free product, Tuple, Exact sequence, Sequence (biology), Product (mathematics), Mathematics, Algebra over a field

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