By combining basic techniques in Lie Theory and a computer algebra tool which is the so-called triangular decomposition, the class of 7-dimensional real and complex indecomposable solvable Lie ...algebras having 5-dimensional nilradicals is classified up to isomorphism. In association with Gong (1998), Parry (2007), Hindeleh and Thompson (2008), we achieve a full classification of 7-dimensional real and complex indecomposable solvable Lie algebras.
The paper is devoted studying solvable Leibniz algebras with a nilradical possessing the codimension equals the number of its generators. We describe this class in non-split nilradical case up to ...isomorphism. Then the case of split nilradical is worked out. We show that the results obtained earlier on this class of Leibniz algebras come as particular cases of the results of this paper. It is shown that such a solvable extension is unique. Finally, we prove that the solvable Leibniz algebras considered are complete.
For a sequence of the naturally graded quasi-filiform Leibniz algebra of second type
introduced by Camacho, Gómez, González and Omirov, all the possible right solvable indecomposable extensions over ...the field
are constructed.
In the paper we describe 5-dimensional solvable Leibniz algebras with three-dimensional nilradical. Since those 5-dimensional solvable Leibniz algebras whose nilradical is three-dimensional ...Heisenberg algebra have been classified before we focus on the rest cases. The result of the paper together with Heisenberg nilradical case gives complete classification of all 5-dimensional solvable Leibniz algebras with three-dimensional nilradical.
Subinvariance in Leibniz algebras Misra, Kailash C.; Stitzinger, Ernie; Yu, Xingjian
Journal of algebra,
02/2021, Letnik:
567
Journal Article
Recenzirano
Odprti dostop
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 subalgebras of Leibniz algebras and study their properties. It is shown that the signature results on subinvariance in Lie algebras have analogs for Leibniz algebras.
Let
R
be a commutative unital ring and
a
∈
R
.
We introduce and study properties of a functor
a
Γ
a
(
-
)
,
called the locally nilradical on the category of
R
-modules.
a
Γ
a
(
-
)
is a ...generalisation of both the torsion functor (also called section functor) and Baer’s lower nilradical for modules. Several local–global properties of the functor
a
Γ
a
(
-
)
are established. As an application, results about reduced
R
-modules are obtained and hitherto unknown ring theoretic radicals as well as structural theorems are deduced.
This work is devoted to the complete classification of solvable Leibniz algebras with the naturally graded quasi-filiform non-Lie nilradical. It should be noted that the class of naturally graded ...quasi-filiform Leibniz algebras is sufficiently large, and solvable Leibniz algebras with the nilradical which is isomorphic to several of these algebras are classified in a series of works. This paper considered all omitted cases and completed the problem of classifying solvable Leibniz algebras with naturally graded quasi-filiform non-Lie nilradical. At the end of the paper we combine all results obtained to date, and provide a complete list of solvable Leibniz algebras, whose nilradical is a naturally graded quasi-filiform Leibniz algebra.
The purpose of this short note is to correct an error which appears in the literature concerning Leibniz algebras L: namely, that
where N(L) is the nilradical of L and I is the Leibniz kernel.
Leibniz superalgebras with nilindex $n + m$ and characteristic sequence
$(n-1, 1 \ | \ m)$ divided into four parametric classes that contain a set of
non-isomorphic superalgebras. In this paper, we ...give a complete classification
of solvable Leibniz superalgebras whose nilradical is a nilpotent Leibniz
superalgebra with nilindex $n + m$ and characteristic sequence $(n-1, 1 \ | \
m)$. We obtain a condition for the value of parameters of the classes of such
nilpotent superalgebras for which they have a solvable extension. Moreover, the
classification of solvable Leibniz superalgebras whose nilradical is a Lie
superalgebra with the maximal nilindex is given.
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