Related papers: Existentially closed Leibniz algebras and an embed…
As mathematical induction is applied to prove statements on natural numbers, {\it continuous induction} (or, {\it real induction}) is a tool to prove some statements in real analysis.(Although, this comparison is somehow an overstatement.)…
We define a canonical relative commutant planar algebra from a strongly Markov inclusion of finite von Neumann algebras. In the case of a connected unital inclusion of finite dimensional C*-algebras with the Markov trace, we show this…
The implication problem for the class of embedded dependencies is undecidable. However, this does not imply lackness of a proof procedure as exemplified by the chase algorithm. In this paper we present a complete axiomatization of embedded…
An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.
A Leibniz class is a class of logics closed under the formation of term-equivalent logics, compatible expansions, and non-indexed products of sets of logics. We study the complete lattice of all Leibniz classes, called the Leibniz…
We axiomatically define (pre-)Hilbert categories. The axioms resemble those for monoidal Abelian categories with the addition of an involutive functor. We then prove embedding theorems: any locally small pre-Hilbert category whose monoidal…
The present paper, though inspired by the use of tensor hierarchies in theoretical physics, establishes their mathematical credentials, especially as genetically related to Lie algebra crossed modules. Gauging procedures in supergravity…
The universal enveloping algebra functor between Leibniz and associative algebras defined by Loday and Pirashvili is extended to crossed modules. We prove that the universal enveloping crossed module of algebras of a crossed module of…
In this paper we describe central extensions of some nilpotent Leibniz algebras. Namely, central extensions of the Leibniz algebra with maximal index of nilpotency are classified. Moreover, non-split central extensions of naturally graded…
Leibniz algebras are certain generalizations of Lie algebras. Motivated by the concept of subinvariance in group theory, Schenkman studied properties of subinvariant subalgebras of a Lie algebra. In this paper we define subinvariant…
In this paper, we investigate linear systems on hyperelliptic varieties. We prove analogues of well-known theorems on abelian varieties, like Lefschetz's embedding theorem and higher k-jet embedding theorems. Syzygy or $N_p$-properties are…
W. A. Moens proved that a Lie algebra is nilpotent if and only if it admits an invertible Leibniz-derivation. In this paper we show that with the definition of Leibniz-derivation from W. A. Moens the similar result for non Lie Leibniz…
The paper is devoted to the so-called complete Leibniz algebras. It is known that a Lie algebra with a complete ideal is split. We will prove that this result is valid for Leibniz algebras whose complete ideal is a solvable algebra such…
In this paper we establish some subnormal embeddings of groups into groups with additional properties; in particular embeddings of countable groups into 2-generated groups with some extra properties. The results obtained are generalizations…
We introduce the enveloping algebra for a Leibniz pair, and show that the category of modules over a Leibniz pair is isomorphic to the category of left modules over its enveloping algebra. Consequently, we show that the cohomology theory…
The aim of this work is to present the description up to isomorphism of Leibniz superalgebras with characteristic sequence (n | m-1, 1) and nilindex n+m.
Lie-Rinehart algebras, also known as Lie algebroids, give rise to Hopf algebroids by a universal enveloping algebra construction, much as the universal enveloping algebra of an ordinary Lie algebra gives a Hopf algebra, of infinite…
This note is about a little extension of Nash's embedding theorem in the case of complete manifolds.
We show that a class of algebras is closed under the taking of homomorphic images and direct products if and only if the class consists of all algebras that satisfy a set of (generally simultaneous) equations. For classes of regular…
We extend conjugacy results from Lie algebras to their Leibniz algebra generalizations. The proofs in the Lie case depend on anti-commutativity. Thus it is necessary to find other paths in the Leibniz case. Some of these results involve…