Solvable Leibniz algebras with NFn⊕ F1m nilradical

All finite-dimensional solvable Leibniz algebras L, having N = NFn⊕ F1m as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described. NFn and F1m are the null-filiform and naturally graded filiform Leibniz algebras of dimensions n and m, respectively. Moreover, we show that these algebras are rigid

On naturally graded Lie and Leibniz superalgebras

In general, the study of gradations has always represented a cornerstone in algebra theory. In particular, \textit{naturally graded} seems to be the first and the most relevant gradation when it comes to nilpotent algebras, a large class of solvable ones. In fact, many families of relevant solvable algebras have been obtained by extensions of naturally graded nilpotent algebras, i.e. solvable algebras with a well-structured nilradical. Thus, the aim of this work is introducing the concept of naturally graded for superalgebra structures such as Lie and (non-Lie) Leibniz. After having defined naturally graded Lie and Leibniz superalgebras, we characterize natural gradations on a very important class of each of them, that is, those with maximal super-nilindex

The derivations of some evolution algebras

In this work we investigate the derivations of n−dimensional complex evolution algebras, depending on the rank of the appropriate matrices. For evolution algebra with non-singular matrices we prove that the space of derivations is zero. The spaces of derivations for evolution algebras with matrices of rank n−1 are described.Junta de Andalucía FQM-14

Central extensions of filiform Zinbiel algebras

In this paper we describe central extensions (up to isomorphism) of all complex null-filiform and filiform Zinbiel algebras. It is proven that every non-split central extension of an $n$-dimensional null-filiform Zinbiel algebra is isomorphic to an $(n+1)$-dimensional null-filiform Zinbiel algebra. Moreover, we obtain all pairwise non isomorphic quasi-filiform Zinbiel algebras.Comment: arXiv admin note: substantial text overlap with arXiv:1809.00183, arXiv:1904.00845, arXiv:1812.01442, arXiv:1803.0769

The variety of dual mock-Lie algebras

summary:We classify all complex $7$- and $8$-dimensional dual mock-Lie algebras by the algebraic and geometric way. Also, we find all non-trivial complex $9$-dimensional dual mock-Lie algebras

Iberian Iron Age pottery with stamped decoration from the settlement at Cerro de la Cruz (Almedinilla, Córdoba)

Presentamos un catálogo, análisis y estudio cronológico y espacial de las cerámicas ibéricas con decoración estampillada procedentes del poblado ibérico del Cerro de la Cruz (Almedinilla), uno de los muy pocos en Andalucía excavados en extensión. Procedentes normalmente de niveles superficiales y muy fragmentadas, al contrario de lo que es normal en las estancias de este poblado destruido violentamente hacia 141 a.C., es posible que estas piezas formen parte de una fase ligeramente más antigua al nivel de destrucción y con vinculaciones con el área de Jaén e incluso la Submeseta SurWe present a detailed catalogue, analysis and chronological study of the pottery with stamped decoration from the excavations at the Iberian Iron Age settlement at Cerro de la Cruz (Almedinilla, Córdoba). These pieces have usually been found in superficial strata and are usually very fragmentary shards, in striking contrast with the usual pattern of almost complete pottery vessels found in the different buildings from the this site, violently destroyed c. 141 BC. It is possible that these productions are part of a slightly earlier chronological phase of the site, and that they have connections with the region of Jaén to the Northeast, and even with the Southern Meseta of the Iberian Peninsul

Leibniz Algebras Constructed by Representations of General Diamond Lie Algebras

In this paper we construct a minimal faithful representation of the (2m + 2)- dimensional complex general Diamond Lie algebra, Dm(C), which is isomorphic to a subalgebra of the special linear Lie algebra sl(m + 2, C). We also construct a faithful representation of the general Diamond Lie algebra Dm which is isomorphic to a subalgebra of the special symplectic Lie algebra sp(2m + 2,R). Furthermore, we describe Leibniz algebras with corresponding (2m + 2)-dimensional general Diamond Lie algebra Dm and ideal generated by the squares of elements giving rise to a faithful representation of Dm.Ministerio de Economía y Competitividad MTM2013-43687-PXunta de Galicia GRC2013-04