An Analytic Method for SS-Expansion involving Resonance and Reduction

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 $0_S$-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.Comment: v3, 47 pages, misprints corrected in Fortschritte der Physik, Published online 7 November 201

Chern-Simons and Born-Infeld gravity theories and Maxwell algebras type

Recently was shown that standard odd and even-dimensional General Relativity can be obtained from a $(2n+1)$-dimensional Chern-Simons Lagrangian invariant under the $B_{2n+1}$ algebra and from a $(2n)$-dimensional Born-Infeld Lagrangian invariant under a subalgebra $\cal{L}^{B_{2n+1}}$ respectively. Very Recently, it was shown that the generalized In\"on\"u-Wigner contraction of the generalized AdS-Maxwell algebras provides Maxwell algebras types $\cal{M}_{m}$ which correspond to the so called $B_{m}$ Lie algebras. In this article we report on a simple model that suggests a mechanism by which standard odd-dimensional General Relativity may emerge as a weak coupling constant limit of a $(2p+1)$-dimensional Chern-Simons Lagrangian invariant under the Maxwell algebra type $\cal{M}_{2m+1}$, if and only if $m\geq p$. Similarly, we show that standard even-dimensional General Relativity emerges as a weak coupling constant limit of a $(2p)$-dimensional Born-Infeld type Lagrangian invariant under a subalgebra $\cal{L}^{\cal{M}_{2m}}$ of the Maxwell algebra type, if and only if $m\geq p$. It is shown that when $m<p$ this is not possible for a $(2p+1)$-dimensional Chern-Simons Lagrangian invariant under the $\cal{M}_{2m+1}$ and for a $(2p)$-dimensional Born-Infeld type Lagrangian invariant under $\cal{L}^{\cal{M}_{2m}}$ algebra.Comment: 30 pages, accepted for publication in Eur.Phys.J.C. arXiv admin note: text overlap with arXiv:1309.006

Generalized Poincare algebras and Lovelock-Cartan gravity theory

We show that the Lagrangian for Lovelock-Cartan gravity theory can be re-formulated as an action which leads to General Relativity in a certain limit. In odd dimensions the Lagrangian leads to a Chern-Simons theory invariant under the generalized Poincar\'{e} algebra $\mathfrak{B}_{2n+1},$ while in even dimensions the Lagrangian leads to a Born-Infeld theory invariant under a subalgebra of the $\mathfrak{B}_{2n+1}$ algebra. It is also shown that torsion may occur explicitly in the Lagrangian leading to new torsional Lagrangians, which are related to the Chern-Pontryagin character for the $B_{2n+1}$ group.Comment: v2: 18 pages, minor modification in the title, some clarifications in the abstract, introduction and section 2, section 4 has been rewritten, typos corrected, references added. Accepted for publication in Physic letters

Generalized cosmological term in D=4 supergravity from a new AdS-Lorentz superalgebra

A new supersymmetrization of the so-called AdS-Lorentz algebra is presented. It involves two fermionic generators and is obtained by performing an abelian semigroup expansion of the superalgebra osp(4|1). The peculiar properties of the aforesaid expansion method are then exploited to construct a D=4 supergravity action involving a generalized supersymmetric cosmological term in a geometric way, only from the curvatures of the novel superalgebra. The action obtained with this procedure is a MacDowell-Mansouri like action. Gauge invariance and supersymmetry of the action are also analyzed.Comment: 25 pages. This is a preprint of the article published in Eur. Phys. J. C 78 (2018) no.11, 945. The final authenticated version is available online at: https://doi.org/10.1140/epjc/s10052-018-6421-

Epidemiological projections for COVID-19 considering lockdown policies and social behavior: the case of Bolivia

We assess the epidemic situation caused by SARS-CoV-2 using Tsallis' proposal for determining the occurrence of the peak, and also the Susceptible-Infected-Recovered-Asymptomatic-Symptomatic and Dead (\textbf{SIRASD}) compartmental model. Using these two models, we determine a range of probable peak dates and study several social distancing scenarios during the epidemic. Due to the socioeconomic situation and the conflictive political climate, we take for our study the case of Bolivia, where a national election was originally scheduled to occur on September 6th and recently rescheduled on October 18th. For this, we analyze both electoral scenarios and show that such an event can largely affect the epidemic's dynamics.Comment: 15 pages, 7 figure

Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras

We show that infinite families of non-relativistic spin-$3$ symmetries in $2+1$ dimensions, which include higher-spin extensions of the Bargmann, Newton-Hooke, non-relativistic Maxwell, and non-relativistic AdS-Lorentz algebras, can be obtained as Lie algebra expansions of two different spin-$3$ extensions of the Nappi-Witten symmetry. These higher-spin Nappi-Witten algebras, in turn, are obtained by means of In\"on\"u-Wigner contractions applied to suitable direct product extensions of $\mathfrak{sl}(3,\mathbb{R})$. Conversely, we show that the same result can be obtained by considering contractions of expanded $\mathfrak{sl}(3,\mathbb{R})$ algebras. The method can be used to define non-relativistic higher-spin Chern-Simon gravity theories in $2+1$ dimensions in a systematic way.Comment: 44 pages, typos corrected, references adde