Lie structure induced by the q-number operator
Abstract
Within the context of the q-deformed harmonic oscillator, the annihilation operator a and the q-number operator N generate an associative algebra of operators, the subspace of which, consisting of all operators that are compact and hollow (possessing a zero diagonal), is equal to the derived algebra of the Lie algebra of operators generated by a and N. Thus, a solution to a Lie polynomial characterization problem is obtained using the operator-theoretic notions of compactness and hollowness.
Fields of Study & Subjects
Advanced Topics in Algebra
Advanced Operator Algebra Research
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Figshare
- Publication date
- 1 January 2026
- Language
- EN
- Document type
- Preprint