Extended D=3D=3 Bargmann supergravity from a Lie algebra expansion

In this paper we show how the method of Lie algebra expansions may be used to obtain, in a simple way, both the extended Bargmann Lie superalgebra and the Chern-Simons action associated to it in three dimensions, starting from $D=3$, $\mathcal{N}=2$ superPoincar\'e and its corresponding Chern-Simons supergravity.Comment: 17 page

Hopf algebras with triality

In this paper we revisit and extend the constructions of Glauberman and Doro on groups with triality and Moufang loops to Hopf algebras. We prove that the universal enveloping algebra of any Lie algebra with triality is a Hopf algebra with triality. This allows us to give a new construction of the universal enveloping algebras of Malcev algebras. Our work relies on the approach of Grishkov and Zavarnitsine to groups with triality.Comment: AMS-LaTeX, 23 pages. To appear in Trans. Amer. Math. So

On a class of n-Leibniz deformations of the simple Filippov algebras

We study the problem of the infinitesimal deformations of all real, simple, finite-dimensional Filippov (or n-Lie) algebras, considered as a class of n-Leibniz algebras characterized by having an n-bracket skewsymmetric in its n-1 first arguments. We prove that all n>3 simple finite-dimensional Filippov algebras are rigid as n-Leibniz algebras of this class. This rigidity also holds for the Leibniz deformations of the semisimple n=2 Filippov (i.e., Lie) algebras. The n=3 simple FAs, however, admit a non-trivial one-parameter infinitesimal 3-Leibniz algebra deformation. We also show that the $n\geq 3$ simple Filippov algebras do not admit non-trivial central extensions as n-Leibniz algebras of the above class.Comment: 19 pages, 30 refs., no figures. Some text rearrangements for better clarity, misprints corrected. To appear in J. Math. Phy

Sabinin AIgebras: The Basis of a Nonassociative Lie Theory

Certain famous concepts and results such as Universal enveloping algebras, Poincaré-Birkhoff-Witt Theorem and the Lie correspondence have been, up to some extend, synonymous of Lie algebras

Depletion of T-cell intracellular antigen proteins promotes cell proliferation

The transcriptome of TIA-1/TIAR-depleted cells indicates roles in inflammation, cell-cell signaling, immune suppression, angiogenesis, metabolism and cell proliferation

Contractions of Filippov algebras

We introduce in this paper the contractions $\mathfrak{G}_c$ of $n$-Lie (or Filippov) algebras $\mathfrak{G}$ and show that they have a semidirect structure as their $n=2$ Lie algebra counterparts. As an example, we compute the non-trivial contractions of the simple $A_{n+1}$ Filippov algebras. By using the \.In\"on\"u-Wigner and the generalized Weimar-Woods contractions of ordinary Lie algebras, we compare (in the $\mathfrak{G}=A_{n+1}$ simple case) the Lie algebras Lie$\,\mathfrak{G}_c$ (the Lie algebra of inner endomorphisms of $\mathfrak{G}_c$) with certain contractions $(\mathrm{Lie}\,\mathfrak{G})_{IW}$ and $(\mathrm{Lie}\,\mathfrak{G})_{W-W}$ of the Lie algebra Lie$\,\mathfrak{G}$ associated with $\mathfrak{G}$.Comment: plain latex, 36 pages. A few misprints corrected. This v3 is actually v2 (v1 had been replaced by itself by error). To appear in J. Math. Phy

Teaching the mean-field approximation

[ENG] Many University subjects that we teach in engineering degrees (e.g. Control Theory, Operations Research, Game Theory, Physics, Fluid Dynamics, Modelling and Control of Queuing and Production Systems, Stochastic Processes, and Network Theory) make extensive use of the so-called mean-field analysis. In these subjects, the mean-field analysis often appears as an approximation of a discrete time stochastic process where a) the inherent stochasticity of the original process is replaced with determinism, and b) the time discreteness of the original process is replaced with time continuity. Thus, the mean-field approximation is presented as a continuous time differential equation that can approximate the dynamics of the discrete time stochastic process under investigation. In this paper we present a teaching methodology that we have found useful for introducing students to the mean-field analysis, and we provide some accompanying teaching material –in the form of computer models– that other academics may want to use in their own lecturesThe authors gratefully acknowledge financial support from the Spanish JCyL (VA006B09, GR251/2009), MICINN (SICOSSYS: TIN2008-06464-C03-02; CONSOLIDER-INGENIO 2010: CSD2010-00034; DPI2010-16920) and L.R.I. from the Spanish Ministry of Education (JC2009-00263)