Abstract
In this paper, we study the strong extension groups of Cuntz–Krieger algebras, and present a formula to compute the groups. We also detect the position of the Toeplitz extension of a Cuntz–Krieger algebra in the strong extension group and in the weak extension group to see that the weak extension group with the position of the Toeplitz extension is a complete invariant of the isomorphism class of the Cuntz–Krieger algebra associated with its transposed matrix.
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Acknowledgement
The author would like to thank Joachim Cuntz for his useful comments and suggestions on a preliminary version of this paper. The author expresses his thanks to the referee for careful reading and lots of helpful advices and suggestions in the presentation of the paper.
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This work was supported by JSPS KAKENHI Grant Number 19K03537.
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Matsumoto, K. On strong extension groups of Cuntz–Krieger algebras. Anal Math (2024). https://doi.org/10.1007/s10476-024-00046-5
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DOI: https://doi.org/10.1007/s10476-024-00046-5
Key words and phrases
- extension group
- \(C^*\)-algebra
- extension
- Cuntz–Krieger algebra
- strong extension group
- Toeplitz extension
- Fredholm index