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We exhibit an operator norm bounded, infinite sequence { A n } \{A_n\} of 3 n × 3 n 3n \times 3n complex matrices for which the commutator map X ↦ X A n − A n X X\mapsto XA_n - A_nX is uniformly bounded below as an operator over the space of trace-zero self-adjoint matrices equipped with Hilbert–Schmidt norm. The construction is based on families of quantum expanders. We give several potential applications of these matrices to the study of quantum expanders. We formulate several natural conjectures and provide numerical evidence.
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This content will become publicly available on March 4, 2026
Numerical semigroups from rational matrices I: power-integral matrices and nilpotent representations
- Award ID(s):
- 2054002
- PAR ID:
- 10582396
- Publisher / Repository:
- Taylor and Francis
- Date Published:
- Journal Name:
- Communications in Algebra
- Volume:
- 53
- Issue:
- 3
- ISSN:
- 0092-7872
- Page Range / eLocation ID:
- 1127 to 1137
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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