2001/03/13 by Fabien Besnard, Besnard, Fabien
Mathematics · Physics and Astronomy · #16Z05 #81R99 #Advanced Topics in Algebra #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Boson #CCR and CAR algebras #FOS: Mathematics #FOS: Physical sciences #Fermion #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Non-associative algebra #Nonlinear Waves and Solitons #Operator (biology) #Operator algebra #Particle physics #Physics #Pure mathematics #Quadratic growth #Quantum Algebra (math.QA) #Symmetry (geometry) #math-ph #math.MP #math.QA #msc:16Z05 #msc:81R99
paper · pdf · doi:10.48550/arxiv.math-ph/0103017
58 pages, no figure
arxiv created 2001/03/13 · openalex publication_date 2001/03/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Under some hypotheses (symmetry, confluence), we enumerate all quadratically presented algebras, generated by creation and destruction operators, in which number operators exist. We show that these are algebras of bosons, fermions, their immediate generalizations that we call pseudo-bosons and pseudo-fermions, and also matrix algebras, in the finitely generated case. We then recover q-bosons (and pseudo-q-bosons) by a completion operation.