2016/09/30 by M. C. Ipinza, F. Lingua, D. M. Peñafiel +1 · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1002/prop.201600094
published as Fortschr. Phys. 64, 854-880 (2016) · v3, 47 pages, misprints corrected in Fortschritte der Physik, Published online 7 November 2016
arxiv created 2016/11/10 · arxiv updated 2016/11/18
In this paper we describe an analytic method able to give the multiplication table(s) of the set(s) involved in an S-expansion process (with either resonance or 0S-resonant-reduction) for reaching a target Lie (super)algebra from a starting one, after having properly chosen the partitions over subspaces of the considered (super)algebras. This analytic method gives us a simple set of expressions to find the partitions over the set(s) involved in the process. Then, we use the information coming from both the initial (super)algebra and the target one for reaching the multiplication table(s) of the mentioned set(s). Finally, we check associativity with an auxiliary computational algorithm, in order to understand whether the obtained set(s) can describe semigroup(s) or just abelian set(s) connecting two (super)algebras. We also give some interesting examples of application, which check and corroborate our analytic procedure and also generalize some result already presented in the literature.