We investigate subalgebras $A$ of the Cuntz algebra ${\mathcal O}_n$ that arise as finite direct sums of corners of the UHF-subalgebra ${\mathcal F}_n$. For such an $A$, we completely determine its normalizer group inside ${\mathcal O}_n$.
References
R. Conti and C. Pinzari, Remarks on the index of endomorphisms of Cuntz algebras, J. Funct. Anal. 142 (1996), 369–405. MR1423039 10.1006/jfan.1996.0154 R. Conti and C. Pinzari, Remarks on the index of endomorphisms of Cuntz algebras, J. Funct. Anal. 142 (1996), 369–405. MR1423039 10.1006/jfan.1996.0154
R. Conti, M. Rørdam and W. Szymański, Endomorphisms of $\mathcal{O}_{n}$ which preserve the canonical UHF-subalgebra. J. Funct. Anal. 259 (2010), 602–617. MR2644099 10.1016/j.jfa.2010.03.027 R. Conti, M. Rørdam and W. Szymański, Endomorphisms of $\mathcal{O}_{n}$ which preserve the canonical UHF-subalgebra. J. Funct. Anal. 259 (2010), 602–617. MR2644099 10.1016/j.jfa.2010.03.027
J. Cuntz, Simple $C^*$-algebras generated by isometries, Commun. Math. Phys. 57 (1977), 173–185. MR467330 10.1007/BF01625776 euclid.cmp/1103901288
J. Cuntz, Simple $C^*$-algebras generated by isometries, Commun. Math. Phys. 57 (1977), 173–185. MR467330 10.1007/BF01625776 euclid.cmp/1103901288
T. Hayashi, On normalizers of $C^{*}$-subalgebras in the Cuntz algebra $\mathcal{O}_{n}$, J. Operator Theory 69 (2013), 525–533. MR3053353 10.7900/jot.2011feb13.1939 T. Hayashi, On normalizers of $C^{*}$-subalgebras in the Cuntz algebra $\mathcal{O}_{n}$, J. Operator Theory 69 (2013), 525–533. MR3053353 10.7900/jot.2011feb13.1939
M. Izumi, Subalgebras of infinite $C^*$–algebras with finite Watatani indices. I. Cuntz algebras, Commun. Math. Phys. 155 (1993), 157–182. MR1228532 10.1007/BF02100056 euclid.cmp/1104253206
M. Izumi, Subalgebras of infinite $C^*$–algebras with finite Watatani indices. I. Cuntz algebras, Commun. Math. Phys. 155 (1993), 157–182. MR1228532 10.1007/BF02100056 euclid.cmp/1104253206
Y. Watatani, Index for $C^*$-subalgebras, Mem. Amer. Math. Soc. 83 (1990), no. 424. MR996807 10.1090/memo/0424 Y. Watatani, Index for $C^*$-subalgebras, Mem. Amer. Math. Soc. 83 (1990), no. 424. MR996807 10.1090/memo/0424
