2009/05/16 by Andrey Kuleshov, A. Kuleshov, Kuleshov, A. +3
Computer Science · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Symbolic Computation (cs.SC) #cs.SC #hep-th #math.QA #math.RT
paper · pdf · doi:10.48550/arxiv.0905.2705
35 pages, 2 figures in eps-format, corrected typos, added references
openalex publication_date 2009/05/16 · arxiv created 2009/08/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We suggest a programming realization of an algorithm for verifying a given set of algebraic relations in the form of a supercommutator multiplication table for the Verma module, which is constructed according to a generalized Cartan procedure for a quadratic superalgebra and whose elements are realized as a formal power series with respect to non-commuting elements. To this end, we propose an algebraic procedure of Verma module construction and its realization in terms of non-commuting creation and annihilation operators of a given Heisenberg--Weyl superalgebra. In doing so, we set up a problem which naturally arises within a Lagrangian description of higher-spin fields in anti-de-Sitter (AdS) spaces: to verify the fact that the resulting Verma module elements obey the given commutator multiplication for the original non-linear superalgebra. The problem setting is based on a restricted principle of mathematical induction, in powers of inverse squared radius of the AdS-space. For a construction of an algorithm resolving this problem, we use a two-level data model within the object-oriented approach, which is realized on a basis of the programming language C#. The program allows one to consider objects (of a less general nature than non-linear commutator superalgebras) that fall under the class of so-called GR-algebras, for whose treatment one widely uses the module Plural of the system Singular of symbolic computations for polynomials.