2016/11/30 by D. M. Peñafiel, L. Ravera · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Abelian group #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebra over a field #Context (archaeology) #Generalization #Homotopy and Cohomology in Algebraic Topology #Ideal (ethics) #Semigroup #Subalgebra #hep-th
paper · pdf · doi:10.1063/1.4991378
published as J. Math. Phys. 58, 081701 (2017) · 43 pages, title and abstract modified to better represent the content, some sections clarified. Version accepted for publication in Journal of Mathematical Physics
openalex publication_date 2017/08/01 · arxiv created 2017/08/04 · arxiv updated 2017/08/18 · openalex created_date 2017/08/31 · openalex updated_date 2026/08/05
According to the literature, the S-expansion procedure involving a finite semigroup is valid no matter what the structure of the original Lie (super)algebra is; however, when something about the structure of the starting (super)algebra is known and when certain particular conditions are met, the S-expansion method (with its features of resonance and reduction) is able not only to lead to several kinds of expanded (super)algebras but also to reproduce the effects of the standard as well as the generalized Inönü-Wigner contraction. In the present paper, we propose a new prescription for S-expansion, involving an infinite abelian semigroup S(∞) and the subtraction of an infinite ideal subalgebra. We show that the subtraction of the infinite ideal subalgebra corresponds to a reduction. Our approach is a generalization of the finite S-expansion procedure presented in the literature, and it offers an alternative view of the generalized Inönü-Wigner contraction. We then show how to write the invariant tensors of the target (super)algebras in terms of those of the starting ones in the infinite S-expansion context presented in this work. We also give some interesting examples of application on algebras and superalgebras.