scholarly journals On the subalgebra lattice of a Leibniz algebra

2021 ◽  
pp. 1-13
Author(s):  
Salvatore Siciliano ◽  
David A. Towers
Keyword(s):  
Leibniz Algebra ◽  
Subalgebra Lattice

scholarly journals Algorithm for Testing the Leibniz Algebra Structure

2009 ◽  
pp. 177-186 ◽  
Author(s):  
José Manuel Casas ◽  
Manuel A. Insua ◽  
Manuel Ladra ◽  
Susana Ladra
Keyword(s):  
Leibniz Algebra ◽  
Algebra Structure

scholarly journals Deformation of Dual Leibniz Algebra Morphisms

2007 ◽  
Vol 35 (4) ◽  
pp. 1369-1378 ◽  
Author(s):  
Donald Yau
Keyword(s):  
Leibniz Algebra

Some Properties of ID∗-n-Lie-derivations of Leibniz algebras

2021 ◽  
pp. 2250054
Author(s):  
G. R. Biyogmam ◽  
C. Tcheka ◽  
D. A. Kamgam
Keyword(s):  
Lie Algebra ◽  
Leibniz Algebra ◽  
Central Series ◽  
Algebra Structure ◽  
Leibniz Algebras ◽  
Lie Derivations

The concepts of [Formula: see text]-derivations and [Formula: see text]-central derivations have been recently presented in [G. R. Biyogmam and J. M. Casas, [Formula: see text]-central derivations, [Formula: see text]-centroids and [Formula: see text]-stem Leibniz algebras, Publ. Math. Debrecen 97(1–2) (2020) 217–239]. This paper studies the notions of [Formula: see text]-[Formula: see text]-derivation and [Formula: see text]-[Formula: see text]-central derivation on Leibniz algebras as generalizations of these concepts. It is shown that under some conditions, [Formula: see text]-[Formula: see text]-central derivations of a non-Lie-Leibniz algebra [Formula: see text] coincide with [Formula: see text]-[Formula: see text]-[Formula: see text]-derivations, that is, [Formula: see text]-[Formula: see text]-derivations in which the image is contained in the [Formula: see text]th term of the lower [Formula: see text]-central series of [Formula: see text] and vanishes on the upper [Formula: see text]-central series of [Formula: see text] We prove some properties of these [Formula: see text]-[Formula: see text]-[Formula: see text]-derivations. In particular, it is shown that the Lie algebra structure of the set of [Formula: see text]-[Formula: see text]-[Formula: see text]-derivations is preserved under [Formula: see text]-[Formula: see text]-isoclinism.

The subalgebra lattice of a Heyting algebra

1987 ◽  
Vol 37 (1) ◽  
pp. 34-41 ◽  
Author(s):  
L. Vrancken-Mawet ◽  
Georges Hansoul
Keyword(s):  
Heyting Algebra ◽  
Subalgebra Lattice

scholarly journals A rigid Leibniz algebra with non-trivial HL2

2020 ◽  
Vol 556 ◽  
pp. 696-724
Author(s):  
Omirov Bakhrom ◽  
Wagemann Friedrich
Keyword(s):  
Leibniz Algebra

scholarly journals ON SEMI-MODULAR SUBALGEBRAS OF LIE ALGEBRAS OVER FIELDS OF ARBITRARY CHARACTERISTIC

2008 ◽  
Vol 01 (02) ◽  
pp. 283-294 ◽  
Author(s):  
DAVID A. TOWERS
Keyword(s):  
Lie Algebras ◽  
Extensive Study ◽  
Two Dimensional ◽  
Perfect Field ◽  
Characteristic P ◽  
Subalgebra Lattice ◽  
Closed Fields ◽  
The One ◽  
Algebraically Closed Fields ◽  
Number Of Authors

This paper is a further contribution to the extensive study by a number of authors of the subalgebra lattice of a Lie algebra. It is shown that, in certain circumstances, including for all solvable algebras, for all Lie algebras over algebraically closed fields of characteristic p > 0 that have absolute toral rank ≤ 1 or are restricted, and for all Lie algebras having the one-and-a-half generation property, the conditions of modularity and semi-modularity are equivalent, but that the same is not true for all Lie algebras over a perfect field of characteristic three. Semi-modular subalgebras of dimensions one and two are characterised over (perfect, in the case of two-dimensional subalgebras) fields of characteristic different from 2, 3.

(Pseudo)digraphs and Leibniz algebra isomorphisms

2018 ◽  
Vol 41 (17) ◽  
pp. 7481-7497 ◽  
Author(s):  
Manuel Ceballos ◽  
Juan Núñez ◽  
Ángel F. Tenorio
Keyword(s):  
Leibniz Algebra
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