Name
Title | ||
|---|---|---|
Programming Realization of Symbolic Computations for Non-linear Commutator Superalgebras over the Heisenberg--Weyl Superalgebra: Data Structures and Processing Methods |
Abstract | ||
|---|---|---|
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 \emph{Plural} of the system \emph{Singular} of symbolic computations for
polynomials. |
Year | Venue | Keywords |
|---|---|---|
2009 | arXiv: High Energy Physics - Theory | anti de sitter,formal power series,data structure,quantum algebra,high energy physics,representation theory,programming language,symbolic computation,data model |
Field | DocType | Volume |
Superalgebra,Verma module,Multiplication table,Quantum mechanics,Symbolic computation,Mathematical induction,Formal power series,Commutator,Commutator (electric),Physics | Journal | abs/0905.2705 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| A. Kuleshov | 1 | 0 | 0.34 |
| A. A. Reshetnyak | 2 | 0 | 0.34 |