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A quasidiagonal C*-algebra with a nonquasidiagonal maximal tensor square
Abstract
We construct a separable unital residually finite-dimensional C*-algebra A whose maximal tensor square contains a proper isometry. In particular, A is quasidiagonal whereas Atmax A is not. The algebra is generated by finite regular representations obtained from congruence quotients of an explicit countable affine group. A property~(T) subgroup determines a diagonal Kazhdan projection in the maximal tensor square. Conjugation by a dilation makes this projection equivalent to a proper subprojection. Strictness is detected by a quasi-regular representation whose two factor restrictions descend to the specified algebra A. We give the norm estimate needed for this descent and construct the proper isometry explicitly.
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BibTeX
@misc{moradi2026quasidiagonal,
title = {{A quasidiagonal $C^*$-algebra with a nonquasidiagonal maximal tensor square}},
author = {Mehdi Moradi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00230},
eprint = {2610.00230},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00230},
}
RIS
TY - UNPB
TI - A quasidiagonal C^*-algebra with a nonquasidiagonal maximal tensor square
AU - Mehdi Moradi
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00230
UR - https://arxiv.org/abs/2610.00230
AB - We construct a separable unital residually finite-dimensional C^*-algebra A whose maximal tensor square contains a proper isometry. In particular, A is quasidiagonal whereas Atmax A is not. The algebra is generated by finite regular representations obtained from congruence quotients of an explicit countable affine group. A property~(T) subgroup determines a diagonal Kazhdan projection in the maximal tensor square. Conjugation by a dilation makes this projection equivalent to a proper subprojection. Strictness is detected by a quasi-regular representation whose two factor restrictions descend to the specified algebra A. We give the norm estimate needed for this descent and construct the proper isometry explicitly.
ER -