1996/09/30 by Michel Rausch de Traubenberg, M. Rausch de Traubenberg, Marcus J. Slupinski +1 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Quantum Mechanics and Non-Hermitian Physics #hep-th
paper · pdf · doi:10.1142/s0217732397003174
published as Mod.Phys.Lett.A12:3051-3066,1997 · 17 pages, LaTex, the algebraic structure is given with more details, unitarity of the respresentation is explicitly checked, references has been added, one author has been added, to appear in Mod. Phys. Lett. A
arxiv created 1997/12/11 · openalex publication_date 1997/12/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Nontrivial extensions of three-dimensional Poincaré algebra, beyond the supersymmetric one, are explicitly constructed. These algebraic structures are the natural three-dimensional generalizations of fractional supersymmetry of order F already considered in one and two dimensions. Representations of these algebras are exhibited, and unitarity is explicitly checked. It is then shown that these extensions generate symmetries which connect fractional spin states or anyons. Finally, a natural classification arises according to the decomposition of F into its product of prime numbers leading to subsystems with smaller symmetries.