## Rocky Mountain Journal of Mathematics

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

Jeffrey L. Boersema

#### 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

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

#### 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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