Abstract
Matrix representations for the q-mutator algebras aa °− qa ° a=1 and aa °− qa ° a= q −2 N are presented and the num ber operators for these cases are derived. In the limits when q=−1+ β 2with β 2⪡1, these algebras can be interpreted as describing small violations of the Pauli exclusion principle for a single level. We show that there is a fundamental difference between the physical implications of these algebras and the one introduced by Ignatiev and Kuzmin and studied recently by Greenberg and this author for the description of a small violation of the Pauli exclusion principle.
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