arXiv subjects
Publications and source records attributed to José Manuel Casas.
We analyze behaviors of generalized forgetful and Daletskii-Takhtajan's functors on perfect objects and crossed modules of Leibniz $n$-algebras. Then we give applications to homology and universal central extensions of Leibniz $n$-algebras.
Magnification bias offers a uniquely powerful and independent route to cosmological information. As a gravitational-lensing observable, it probes galaxy-matter correlations without relying on galaxy shapes, PSF modelling, or intrinsic-alignment corrections. Its sensitivity spans both geometry and growth: magnification bias simultaneously responds to the matter density, the amplitude of structure, and the redshift evolution of dark energy (DE) below $z \leq 1$. Importantly, its parameter degeneracy directions differ from those of shear, Baryon Acoustic Oscillations (BAO), and Cosmic Microwave Background (CMB) data, making it a complementary and consistency-check probe with substantial diagnostic value for the next decade of precision cosmology. However, the current potential of magnification bias is restricted by limited sky coverage, catalogue inhomogeneities, and insufficiently precise redshift or number-count characterisation. A next-generation wide-field submillimetre facility like AtLAST -- capable of uniform, deep surveys and spectroscopic mapping -- would overcome these limitations and transform magnification bias into a competitive, high-precision cosmological tool.
Magnification bias, the lensing-induced modification of background source number counts, provides a uniquely powerful probe of the mass density profiles of galaxies and clusters down to kpc scales. Unlike shear-based weak lensing, magnification bias does not rely on galaxy shapes and thus avoids dominant small-scale systematics. Existing studies, however, are limited by sky coverage, positional uncertainty, and insufficiently deep, confusion-limited submillimetre (submm) surveys. A next-generation wide-field, high-throughput submm facility like the proposed 50m-telescope AtLAST is required to unlock this technique's full diagnostic power.
Strong gravitational lensing is a powerful probe of cosmology, dark matter (DM), and high-redshift galaxy evolution, but current samples of strongly lensed galaxies (SLGs) remain far too small to exploit its full potential. $\textit{Herschel}$'s submillimeter (submm) surveys demonstrated that submm selection provides the most efficient and least biased route to identifying high-redshift SLGs, yet produced only a few hundred systems over limited, heterogeneous fields. Achieving the thousands of SLGs required for precision cosmology and detailed studies of distant dusty star-forming galaxies demands a new, wide-area, homogeneous sub-mm survey. A facility like AtLAST, capable of extending $\textit{Herschel}$-like methodologies to much larger areas, is uniquely positioned to deliver the order-of-magnitude increase in SLG numbers needed for transformative progress.
We introduce and study a non-abelian tensor product of two algebras with bracket with compatible actions on each other. We investigate its applications to the universal central extensions and the low-dimensional homology of perfect algebras with bracket.
The main goal of this work, the second in a three-paper series, is to test the impact of a methodological improvement in measuring the magnification bias signal on a sample of submillimeter galaxies and its implications for constraining cosmological parameters. The analysis considers the angular cross-correlation function between a foreground sample of GAMA galaxies ($0.2<z<0.8$) and a background sample of H-ATLAS submillimeter galaxies ($1.2<z<4.0$). A refined methodology, discussed extensively in Paper I, is used. By interpreting the weak lensing signal within the halo model and employing an MCMC algorithm, the posterior distribution of the halo occupation distribution (HOD) and cosmological parameters is obtained for a flat $Λ$CDM model. The analysis incorporates the foreground angular auto-correlation function to account for galaxy clustering. The results demonstrate a remarkable improvement in uncertainties for both HOD and cosmological parameters compared to previous studies. However, when using the cross-correlation data alone, the estimation of $σ_8$ depends on prior knowledge of $β$, the logarithmic slope of the background number counts. Assuming a physically motivated prior distribution for $β$, mean values of $Ω_m=0.18^{+0.03}{-0.03}$ and $σ_8=1.04^{+0.11}{-0.07}$ are obtained. These results may however be subject to an inherent bias in the data due to anomalous behavior observed in the G15 field. After excluding the G15 region, the mean values shift to $Ω_m=0.30^{+0.05}{-0.06}$ and $σ_8=0.92^{+0.07}{-0.07}$. This becomes more apparent when adding the clustering of the foreground sample, but the dependence on $β$ information disappears, mitigating the aforementioned issue. Excluding the G15 region, the joint analysis yields mean values of $Ω_m=0.36^{+0.03}{-0.07}$, $σ_8=0.90^{+0.03}{-0.03}$, and $h=0.76^{+0.14}_{-0.14}$.
Magnification bias, an observational effect of gravitational lensing in the weak regime, allows testing the cosmological model through angular correlations of sources at different redshifts. This effect has been observed in various contexts, particularly with sub-millimeter galaxies (SMGs), offering astrophysical and cosmological insights. The study aims to investigate the magnification bias effect exerted by galaxy clusters on SMGs and its implications for astrophysical and cosmological parameters within the $Λ$CDM model. Magnification bias was explored through quantifying the cross-correlation function, utilised to derive constraints on cosmological and astrophysical parameters with a Markov Chain Monte Carlo algorithm. Two distinct galaxy cluster samples were used to assess result robustness and understand the influence of sample characteristics. Cluster samples show higher cross-correlation values than galaxies, with an excess at larger scales suggesting contributions from additional large-scale structures. The parameters obtained, while consistent with galaxies, are less constrained due to broader redshift distributions and limited cluster statistics. Results align with weak lensing studies, hinting at slightly lower $σ_8$ and $Ω_m$ values than \emph{Planck}'s CMB data, emphasizing the need for enhanced precision and alternative low-redshift universe tests. While yielding constraints compatible with the $Λ$CDM model, limitations include broader redshift distributions and a limited number of lenses, resulting in less constrained parameters compared to previous galaxy studies. Nonetheless, the study underscores the potential of using galaxy clusters as lenses for magnification bias studies, capitalising on their elevated mass, providing a promising avenue to test current Cosmology theories. Further progress can be made by expanding the lens sample size.
We study the extensibility problem of a pair of derivations associated with an abelian extension of algebras with bracket, and derive an exact sequence of the Wells type. We introduce crossed modules for algebras with bracket and prove their equivalence with internal categories in the category of algebras with bracket. We interpret the set of equivalence classes of crossed extensions as the second cohomology. Finally, we construct an eight term exact sequence in the cohomology of algebras with bracket.
We study some properties on $\mathsf{Lie}$-centroids related to central $\mathsf{Lie}$-derivations, generalized $\mathsf{Lie}$-derivations and almost inner $\mathsf{Lie}$-derivations. We also determine the $\mathsf{Lie}$-centroid of the tensor product of a commutative associative algebra and a Leibniz algebra.
A Hom-Lie algebra $(L, α_L)$ is said to be capable if there exists a Hom-Lie algebra $(H, α_H)$ such that $L \cong H/Z(H)$. We obtain a characterisation of capable Hom-Lie algebras involving its epicentre and we use this theory to further study the six-term exact sequence in homology and to obtain a Hopf-type formulae of the second homology of perfect Hom-Lie algebras.
We study the representability of actions in the category of crossed modules of dialgebras via tetramultipliers. We deduce a pair of dialgebras in order to construct an object which, under certain circumstances, is the actor (also known as the split extension classifier). Moreover, we give give a full description of actions in terms of equations. Finally, we check that under the aforementioned circumstances, the center coincides with the kernel of the canonical map from a crossed module to its actor.
In this article we investigate the interplay between stem covers, the Schur multiplier of Leibniz crossed modules and the non-abelian exterior product of Leibniz algebras. In concrete, we obtain a six-term exact sequence associated to a central extension of Leibniz crossed modules, which is useful to characterize stem covers. We show the existence of stem covers and determine the structure of all stem covers of Leibniz crossed modules. Also, we give the connection between the stem cover of a Lie crossed module in the categories of Lie and Leibniz crossed modules respectively.
In this paper, we present a methodology for off-line handwritten character recognition. The proposed methodology relies on a new feature extraction technique based on structural characteristics, histograms and profiles. As novelty, we propose the extraction of new eight histograms and four profiles from the $32\times 32$ matrices that represent the characters, creating 256-dimension feature vectors. These feature vectors are then employed in a classification step that uses a $k$-means algorithm. We performed experiments using the NIST database to evaluate our proposal. Namely, the recognition system was trained using 1000 samples and 64 classes for each symbol and was tested on 500 samples for each symbol. We obtain promising accuracy results that vary from 81.74\% to 93.75\%, depending on the difficulty of the character category, showing better accuracy results than other methods from the state of the art also based on structural characteristics.
We extend to the category of crossed modules of Leibniz algebras the notion of biderivation via the action of a Leibniz algebra. This results into a pair of Leibniz algebras which allow us to construct an object which is the actor under certain circumstances. Additionally, we give a description of an action in the category of crossed modules of Leibniz algebras in terms of equations. Finally, we check that, under the aforementioned conditions, the kernel of the canonical map from a crossed module to its actor coincides with the center and we introduce the notions of crossed module of inner and outer biderivations.
Adjoint functors between the categories of crossed modules of dialgebras and Leibniz algebras are constructed. The well-known relations between the categories of Lie, Leibniz, associative algebras and dialgebras are extended to the respective categories of crossed modules.
We define a category $\galt$ of g-alternative algebras over a field $F$ and present the category of alternative algebras $\alt$ as a full subcategory of $\galt$; in the case $\ch F\neq 2$, we have $\alt=\galt$. For any g-alternative algebra $A$ we give a construction of a universal strict general actor $\cB(A)$ of $A$. We define the subset $\asoci(A)$ of $A$, and show that it is a $\cB(A)$-substructure of $A$. We prove that if $\asoci(A)=0$, then there exists an actor of $A$ in $\galt$ and $\act(A)=\cB(A)$. In particular, we obtain that if $A$ is anticommutative and $\ann(A)=0$, then there exists an actor of $A$ in $\galt$; from this, under the same conditions, we deduce the existence of an actor in $\alt$.