2009/12/14 by P. G. Castro, B. Chakraborty, Biswajit Chakraborty +4 · 5 citations
Mathematics · Physics and Astronomy · #Abelian group #Algebra over a field #Algebraic structures and combinatorial models #Current algebra #Geometry #Hopf algebra #Lie superalgebra #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Superalgebra #Supergravity #Supersymmetry #Supersymmetry algebra #Twist #hep-th #math-ph #math.MP
paper · pdf · doi:10.2478/s11534-010-0078-9
published in Open Physics 9(3), 841-851 (De Gruyter Open) · 18 pages; two references added
arxiv created 2009/12/14 · openalex publication_date 2010/10/05 · arxiv updated 2011/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract The N-extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even N one can identify the 1D N-extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist-deformed (anti)commutators. The main differences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed.