Results 71 to 80 of about 39,924 (177)

Leibniz Representations of Lie Algebras

Journal of Algebra, 1996
The authors examine the category \(L({\mathfrak g})\) of finite-dimensional Leibniz representation [the authors, Math. Ann. 296, 139-158 (1993; Zbl 0821.17022)] of the finite-dimensional semisimple Lie algebra \({\mathfrak g}\). First, they notice that \(L({\mathfrak g})\) is not semisimple even when the characteristic of the field \(k\) is 0.
Loday, J-L, Pirashvili, T
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AGGREGATION AND BRACKETS IN MODERN MATHEMATICS: INTRODUCTION TO LOGICALSEMIOTIC ANALYSIS

Докса, 2015
The article is a logical-methodological investigation in semiotic history of mathematics. It is studied in the article the history of meanings of designation of aggregation and using of brackets and other parentheses in mathematics. The term “aggregation”
Тарас Шиян
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On Soft Intersection Leibniz Algebras

Indian Journal of Pure and Applied Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Odd Jacobi Manifolds and Loday-Poisson Brackets

Journal of Mathematics, 2014
We construct a nonskew symmetric version of a Poisson bracket on the algebra of smooth functions on an odd Jacobi supermanifold. We refer to such Poisson-like brackets as Loday-Poisson brackets.
Andrew James Bruce
doaj   +1 more source

On Leibniz algebras, whose subideals are ideals

Доповiдi Нацiональної академiї наук України
We obtain a description of solvable Leibniz algebras, whose subideals are ideals. A description of certain types of Leibniz T-algebras is also obtained. In particular, it is established that the structure of Leibniz T-algebras essentially depends on the
L.A. Kurdachenko, I.Ya. Subbotin, V.S. Yashchuk   +2 more
doaj   +1 more source

Para-Associative Algebroids

Mathematics
We introduce para-associative algebroids as vector bundles whose sections form a ternary algebra with a generalised form of associativity. We show that a necessary and sufficient condition for local triviality is the existence of a differential ...
Andrew James Bruce
doaj   +1 more source

Steinberg–Leibniz algebras and superalgebras

Journal of Algebra, 2005
The Steinberg Lie algebra \({\mathfrak s}{\mathfrak t}(n,A)\), \(n\geq 3\), over a unital associative algebra \(A\) is the universal central extension of the matrix Lie algebra \({\mathfrak s}{\mathfrak l}(n,A)\), and the Leibniz algebra \({\mathfrak s}{\mathfrak t}{\mathfrak l}(n,A)\) has a similar property in the category of Leibniz algebras.
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Almost-reductive and almost-algebraic Leibniz algebra

International Electronic Journal of Algebra
This paper examines whether the concept of an almost-algebraic Lie algebra developed by Auslander and Brezin in [J. Algebra, 8(1968), 295-313] can be introduced for Leibniz algebras. Two possible analogues are considered: almost-reductive and almost-algebraic Leibniz algebras.
openaire   +4 more sources

A rigid Leibniz algebra with non-trivial HL^2

, 2019
In this article, we generalize Richardson's example of a rigid Lie algebra with non-trivial $H^2$ to the Leibniz setting. Namely, we consider the hemisemidirect product ${\mathfrak h}$ of a semidirect product Lie algebra $M_k\rtimes{\mathfrak g}$ of a ...
Omirov, Bakhrom, Wagemann, Friedrich
core  

2-recognizeable classes of Leibniz algebras

Journal of Algebra, 2015
We show that for fields that are of characteristic 0 or algebraically closed of characteristic greater than 5, that certain classes of Leibniz algebras are 2-recognizeable. These classes are solvable, strongly solvable and super solvable. These results hold in Lie algebras and in general for groups.
Tiffany Burch, Meredith Harris, Allison McAlister, Elyse Rogers, Ernie Stitzinger, S. McKay Sullivan   +5 more
openaire   +2 more sources