Rocky Mountain Journal of Mathematics

The $K$-theory of real graph $C*$-algebras

Jeffrey L. Boersema

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Abstract

In this paper, we will introduce real graph algebras and develop the theory to the point of being able to calculate the $K$-theory of such algebras. The $K$-theory situation is significantly more complicated than in the case for complex graph algebras. To develop the long exact sequence to compute the $K$-theory of a real graph algebra, we need to develop a generalized theory of crossed products for real C*-algebras for groups with involution. We also need to deal with the additional algebraic intricacies related to the period-8 real $K$-theory using united $K$-theory. Ultimately, we prove that the $K$-theory of a real graph algebra is recoverable from the $K$-theory of the corresponding complex graph algebra.

Article information

Source
Rocky Mountain J. Math., Volume 44, Number 2 (2014), 397-417.

Dates
First available in Project Euclid: 4 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1407154906

Digital Object Identifier
doi:10.1216/RMJ-2014-44-2-397

Mathematical Reviews number (MathSciNet)
MR3240506

Zentralblatt MATH identifier
1302.46057

Subjects
Primary: 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]

Keywords
Graph Algebras $K$-theory real C*-algebras

Citation

Boersema, Jeffrey L. The $K$-theory of real graph $C*$-algebras. Rocky Mountain J. Math. 44 (2014), no. 2, 397--417. doi:10.1216/RMJ-2014-44-2-397. https://projecteuclid.org/euclid.rmjm/1407154906


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References

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