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J. M. Casas

Publications and source records attributed to J. M. Casas.

At least 37 records · Page 2Linked to original sources
arXiv2021

Galaxy cluster mass density profile derived using the submillimetre galaxies magnification bias

In this work we want to study the average mass density profile of tens to hundreds of clusters of galaxies acting as lenses that produce a magnification bias on the SMGs, and to estimate their associated masses and concentrations for different richness ranges. The background sample is composed of SMGs observed by Herschel with 1.2<z<4.0 (mean redshift at ~2.3) while the foreground sample is made up of galaxy clusters extracted from the SDSS III with photometric redshifts of 0.05< z< 0.8 (mean redshift at ~0.38). Measurements are obtained by stacking the SMG--cluster pairs to estimate the cross-correlation function using the Davis-Peebles estimator. This methodology allows us to derive the mass density profile for a wide range of angular scales, ~2-250 arcsec or ~10-1300 kpc for z=0.38, with a high radial resolution. We find that It is impossible to fit the data with a single mass density profile at all scales. As for the outer part, the estimated average masses increase from $M_{200c}=5.8$ to $51.5\times 10^{13} M_\odot$ and the concentration parameter from C=0.74 to 1.74. In the small-scale regions, the obtained average masses fluctuate around $M_{200c}=3-4 \times 10^{13}M_\odot$ with average C~4. The total average masses are in perfect agreement with the M-R relationship estimated from the cluster catalogue. While the estimated average C values of the central galactic halos are in agreement with traditional M-C relationships, we find low concentrations for the outer part. Moreover, C decrease for lower R values, probably indicating that the group of galaxies cannot be considered to be relaxed systems. Finally, we notice a systematic lack of signal at the transition between the dominance of the cluster halo and the central galactic halo (~100 kpc). This feature is also present in previous studies using different catalogues and/or methodologies, but is never discussed.

astro-ph.CO↗
arXiv2019

Lie-central derivations, Lie-centroids and Lie-stem Leibniz algebras

In this paper, we introduce the notion Lie-derivation. This concept generalizes derivations for non-Lie Leibniz algebras. We study these Lie-derivations in the case where their image is contained in the Lie-center, call them Lie-central derivations. We provide a characterization of Lie-stem Leibniz algebras by their Lie-central derivations, and prove several properties of the Lie algebra of Lie-central derivations for Lie-nilpotent Leibniz algebras of class 2. We also introduce ${\sf ID}_*-Lie$-derivations. A ${\sf ID}_*-Lie$-derivation of a Leibniz algebra G is a Lie-derivation of G in which the image is contained in the second term of the lower Lie-central series of G, and that vanishes on Lie-central elements. We provide an upperbound for the dimension of the Lie algebra $ID_*^{Lie}(G)$ of $ID_*Lie$-derivation of G, and prove that the sets $ID_*^{Lie}(G)$ and $ID_*^{Lie}(G)$ are isomorphic for any two Lie-isoclinic Leibniz algebras G and Q.

math.RA↗
arXiv2018

A study of $n$-Lie-isoclinic Leibniz algebras

In this paper we introduce the concept of $n$-Lie-isoclinism on non-Lie Leibniz algebras. Among the results obtained, we provide several characterizations of $n$-Lie-isoclinic classes of Leibniz algebras. Also, we provide a characterization of $n$-Lie-stem Leibniz algebras, and prove that every $n$-Lie-isoclinic class of Leibniz algebras contains a $n$-Lie-stem Leibniz algebra.

math.RA↗
arXiv2017

The c-Nilpotent Shur Lie-Multiplier of Leibniz Algebras

We introduce the notion of c-nilpotent Schur Lie-multiplier of Leibniz algebras. We obtain exact sequences and formulas of the dimensions of the underlying vector spaces relating the c-nilpotent Schur Lie-multiplier of a Leibniz algebra Q and its quotient by a two-sided ideal. These tools are used to characterize Lie-nilpotency and c-Lie-stem covers of Leibniz algebras. We prove the existence of c-Lie-stem covers for finite dimensional Leibniz algebras and the non existence of c-covering on certain Lie-nilpotent Leibniz algebras with non trivial c-nilpotent Schur Lie-multiplier, and we provide characterizations of c-Lie-capability of Leibniz algebras by means of both their c-Lie-characteristic ideal and c-nilpotent Schur Lie-multiplier.

math.RA↗
arXiv2017

Markov processes of cubic stochastic matrices: {\it Quadratic stochastic processes}

We consider Markov processes of cubic stochastic (in a fixed sense) matrices which are also called quadratic stochastic process (QSPs). A QSP is a particular case of a continuous-time dynamical system whose states are stochastic cubic matrices satisfying an analogue of the Kolmogorov-Chapman equation (KCE). Since there are several kinds of multiplications between cubic matrices we have to fix first a multiplication and then consider the KCE with respect to the fixed multiplication. Moreover, the notion of stochastic cubic matrix also varies depending on the real models of application. The existence of a stochastic (at each time) solution to the KCE provides the existence of a QSP. In this paper, our aim is to construct QSPs for two specially chosen notions of stochastic cubic matrices and two multiplications of such matrices (known as Maksimov's multiplications). We construct a wide class of QSPs and give some time-dependent behavior of such processes. We give an example with applications to the Biology, constructing a QSP which describes the time behavior (dynamics) of a population with the possibility of twin births.

math.PR↗
arXiv2017

The Schur Lie-Multiplier of Leibinz Algebras

For a free presentation $0 \to R \to F \to G \to 0$ of a Leibniz algebra $G$, the Baer invariant ${\cal M}^{\sf Lie}(G) = \frac{R \cap [F, F]_{Lie}}{[F, R]_{Lie}}$ is called the Schur multiplier of $G$ relative to the Liezation functor or Schur Lie-multiplier. For a two-sided ideal $N$ of a Leibniz algebra $G$, we construct a four-term exact sequence relating the Schur Lie-multiplier of $G$ and $G/N$, which is applied to study and characterize Lie-nilpotency, Lie-stem covers and Lie-capability of Leibniz algebras.

math.RA↗
arXiv2016

Universal $α$-central extensions of hom-Leibniz $n$-algebras

We construct homology with trivial coefficients of Hom-Leibniz $n$-algebras. We introduce and characterize universal ($α$)-central extensions of Hom-Leibniz $n$-algebras. In particular, we show their interplay with the zeroth and first homology with trivial coefficients. When $n=2$ we recover the corresponding results on universal central extensions of Hom-Leibniz algebras. The notion of non-abelian tensor product of Hom-Leibniz $n$-algebras is introduced and we establish its relationship with the universal central extensions. We develop a generalization of the concept and properties of unicentral Leibniz algebras to the setting of Hom-Leibniz $n$-algebras.

math.RA↗
arXiv2016

A non-abelian tensor product of Hom-Lie algebras

Non-abelian tensor product of Hom-Lie algebras is constructed and studied. This tensor product is used to describe universal ($α$-)central extensions of Hom-Lie algebras and to establish a relation between cyclic and Milnor cyclic homologies of Hom-associative algebras satisfying certain additional condition.

math.RA↗
arXiv2016

On Lie-isoclinic Leibniz algebras

In this paper we study the notion of isoclinism on Lie-central extensions of Leibniz algebras, this yields to introduce the concept of Lie-isoclinic Leibniz algebras. We provide several equivalent conditions under which Leibniz algebras are Lie-isoclinic. We also define the concept of Schur Lie-multiplier and analyze its connection with Lie-isoclinism.

math.RA↗
arXiv2016

A non-abelian Hom-Leibniz tensor product and applications

The notion of non-abelian Hom-Leibniz tensor product is introduced and some properties are established. This tensor product is used in the description of the universal ($α$-)central extensions of Hom-Leibniz algebras. We also give its application to the Hochschild homology of Hom-associative algebras.

math.RA↗
arXiv2015

On Lie-central extensions of Leibniz algebras

Basing ourselves on the categorical notions of central extensions and commutators in the framework of semi-abelian categories relative to a Birkhoff subcategory, we study central extensions of Leibniz algebras with respect to the Birkhoff subcategory of Lie algebras, called Lie-central extensions. We obtain a six-term exact homology sequence associated to a Lie-central extension. This sequence, together with the relative commutators, allows us to characterize several classes of Lie-central extensions, such as Lie-trivial, Lie-stem and Lie-stem cover, to introduce and characterize Lie-unicentral, Lie-capable, Lie-solvable and Lie-nilpotent Leibniz algebras.

math.RA↗
arXiv2014

On nilpotent index and dibaricity of evolution algebras

An evolution algebra corresponds to a quadratic matrix $A$ of structural constants. It is known the equivalence between nil, right nilpotent evolution algebras and evolution algebras which are defined by upper triangular matrices $A$. We establish a criterion for an $n$-dimensional nilpotent evolution algebra to be with maximal nilpotent index $2^{n-1}+1$. We give the classification of finite-dimensional complex evolution algebras with maximal nilpotent index. Moreover, for any $s=1,...,n-1$ we construct a wide class of $n$-dimensional evolution algebras with nilpotent index $2^{n-s}+1$. We show that nilpotent evolution algebras are not dibaric and establish a criterion for two-dimensional real evolution algebras to be dibaric.

math.RA↗
arXiv2014

On Algebraic properties of ABO-Blood Type Inheritance Pattern

We generate an algebra on blood phenotypes with multiplication based on human ABO-blood type inheritance pattern. We assume that during meiosis gametes are not chosen randomly. For this algebra we investigate its algebraic properties. Namely, the lattice of ideals and the associative enveloping algebra are described.

math.RA↗
arXiv2013

On the univeral α-central extensions of the semi-direct product of Hom-Leibniz algebras

We introduce Hom-actions, semi-direct product and establish the equivalence between split extensions and the semi-direct product extension of Hom-Leibniz algebras. We analyze the functorial properties of the universal (α)-central extensions of (α)-perfect Hom-Leibniz algebras. We establish under what conditions an automorphism or a derivation can be lifted in an α-cover and we analyze the universal α-central extension of the semi-direct product of two α-perfect Hom-Leibniz algebras.

math.RA↗
arXiv2012

On the degenerations of solvable Leibniz algebras

The present paper is devoted to the description of rigid solvable Leibniz algebras. In particular, we prove that solvable Leibniz algebras under some conditions on the nilradical are rigid and we describe four-dimensional solvable Leibniz algebras with three-dimensional rigid nilradical. We show that the Grunewald-O'Halloran's conjecture "any $n$-dimensional nilpotent Lie algebra is a degeneration of some algebra of the same dimension" holds for Lie algebras of dimensions less than six and for Leibniz algebras of dimensions less than four. The algebra of level one, which is omitted in the 1991 Gorbatsevich's paper, is indicated.

math.AG↗
arXiv2012

On universal central extensions of Hom_Leibniz algebras

In the category of Hom-Leibniz algebras we introduce the notion of representation as adequate coefficients to construct the chain complex to compute the Leibniz homology of Hom-Leibniz algebras. We study universal central extensions of Hom-Leibinz algebras and generalize some classical results, nevertheless it is necessary to introduce new notions of $α$-central extension, universal $α$-central extension and $α$-perfect Hom-Leibniz algebra. We prove that an $α$-perfect Hom-Lie algebra admits a universal $α$-central extension in the categories of Hom-Lie and Hom-Leibniz algebras and we obtain the relationships between both. In case $α= Id$ we recover the corresponding results on universal central extensions of Leibniz algebras.

math.RA↗