Related papers: Linear extensions and nilpotence for Maltsev theor…

We construct homology with trivial coefficients of Hom-Leibniz $n$-algebras. We introduce and characterize universal ($\alpha$)-central extensions of Hom-Leibniz $n$-algebras. In particular, we show their interplay with the zeroth and first…

Moens proved that a finite-dimensional Lie algebra over field of characteristic zero is nilpotent if and only if it has an invertible Leibniz-derivation. In this article we prove the analogous results for finite-dimensional Malcev, Jordan,…

The main purpose of this paper is to prove that the extensions of a nilpotent block algebra and its Glauberman correspondent block algebra are Morita equivalent under an additional group-theoretic condition. In particular, Harris and…

This work is devoted to the classification of solvable Leibniz algebras with an abelian nilradical. We consider $k-1$ dimensional extension of $k$-dimensional abelian algebras and classify all $2k-1$-dimensional solvable Leibniz algebras…

Classical affine Lie algebras appear e.g. as symmetries of infinite dimensional integrable systems and are related to certain differential equations. They are central extensions of current algebras associated to finite-dimensional Lie…

Regular abelian semigroups are isomorphic to a direct product of an abelian group and a rectangular band (Warne, 1994). Seeking for a similar result for nilpotency, solvability and supernilpotency of regular semigroups, we obtain that…

We describe absolute nilpotent and some idempotent elements of an $n$- dimensional evolution algebra corresponding to two permutations and we decompose such algebras to the direct sum of evolution algebras corresponding to cycles of the…

In this paper, using the notions of perturbation and contraction of Lie and Leibniz algebras, we show that the algebraic varieties of Leibniz and nilpotent Leibniz algebras of dimension greater than 2 are reducible.

In this paper we consider Idempotent Functional Analysis, an `abstract' version of Idempotent Analysis developed by V. P. Maslov and his collaborators. We give a review of the basic ideas of Idempotent Analysis. The correspondence between…

We give the algebraic classification of alternative, left alternative, Jordan, bicommutative, left commutative, assosymmetric, Novikov and left symmetric central extensions of null-filiform associative algebras.

We conjecture that the "nilpotent points" of Calogero-Moser space for reflection groups are parametrised naturally by the two-sided cells of the group with unequal parameters. The nilpotent points correspond to blocks of restricted…

We consider continuous extensions of minimal rotations on a locally connected compact group X by arbitrary locally compact Lie groups and prove regularity (i.e. the existence of orbit closures which project onto the whole basis X) in…

The paper studies nilpotent $n$-Lie superalgebras. More specifically speaking, we first prove Engel's theorem for $n$-Lie superalgebras. Second, we research some properties of nilpotent $n$-Lie superalgebras, Finally, we give several…

We present a short introductory overview of the non-commutative extensions of several classical physical theories. After a general discussion of the reasons that suggest that the non-commutativity is a major issue that will eventually lead…

In this paper we show that every finite-dimensional Zinbiel algebra over an arbitrary field is nilpotent, extending a previous result by other authors that they are solvable.

Higher dimensional central extensions of groups were introduced by G. Janelidze as particular instances of the abstract notion of covering morphism from categorical Galois theory. More recently, the notion has been extended to and studied…

We describe explicitly the vertex algebra of (twisted) chiral differential operators on certain nilmanifolds and construct their logarithmic modules. This is achieved by generalizing the construction of vertex operators in terms of…

In this paper we study the tensor product for MV-algebras, the algebraic structures of \L ukasiewicz $\infty$-valued logic. Our main results are: the proof that the tensor product is preserved by the categorical equivalence between the…

We present a functorial construction which, starting from a congruence $\alpha$ of finite index in an algebra A, yields a new algebra C with the following properties: the congruence lattice of C is isomorphic to the interval of congruences…

We obtain a local central limit theorem for cocycles associated with a class of non abelian and non compact group extensions of Gibbs Markov maps. This class consists of multidimensional infinite dihedral groups. Unlike in the set up of the…