1995/12/06 by S. E. Konstein, M. A. Vasiliev
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Quantum Mechanics and Non-Hermitian Physics #hep-th
paper · pdf · doi:10.1063/1.531544
published as J.Math.Phys. 37 (1996) 2872-2891 · 22 pages, LATEX
arxiv created 1995/12/06 · openalex publication_date 1996/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We define a complete set of supertraces on the algebra SHN(ν), the algebra of observables of the N-body rational Calogero model with harmonic interaction. This result extends the previously known results for the simplest cases of N=1 and N=2 to arbitrary N. It is shown that SHN(ν) admits q(N) independent supertraces, where q(N) is a number of partitions of N into a sum of odd positive integers, so that q(N)≳1 for N≥3. Some consequences of the existence of several independent supertraces of SHN(ν) are discussed, such as the existence of ideals in associated W∞-type Lie superalgebras.