1996/12/07 by Mikhail Plyushchay, MIKHAIL S. PLYUSHCHAY · 37 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebra representation #Cellular algebra #Context (archaeology) #Current algebra #Filtered algebra #Integer (computer science) #Mathematical Analysis and Transform Methods #Nonlinear Waves and Solitons #Operator algebra #Quantum Mechanics and Non-Hermitian Physics #Spinor #Universal enveloping algebra #cond-mat #hep-th #math.QA #q-alg
paper · pdf · doi:10.1142/s0217732396002927
published in Modern Physics Letters A 11(37), 2953-2964 (World Scientific) · 11 pages, LaTeX
openalex publication_date 1996/12/07 · arxiv created 1997/01/14 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
It is shown that the deformed Heisenberg algebra involving the reflection operator R (R-deformed Heisenberg algebra) has finite-dimensional representations which are equivalent to representations of para-Grassmann algebra with a special differentiation operator. Guon-like form of the algebra, related to the generalized statistics, is found. Some applications of revealed representations of the R-deformed Heisenberg algebra are discussed in the context of OSp(2|2) supersymmetry. It is shown that these representations can be employed for realizing (2+1)-dimensional supersymmetry. They also give a possibility to construct a universal spinor set of linear differential equations describing either fractional spin fields (anyons) or ordinary integer and half-integer spin fields in 2+1 dimensions.