Related papers: Lie's Theorem for Supertropical Algebra
We introduce the notion of a Lie-like algebra$^{\diamond}$ (superalgebra$^{\diamond}$) for $\diamond\in\{^{1-st}, ^{2-nd}, ^{3-rd} \}$.
We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.
We give a short tour through major parts of a recent long paper [IKR1] on supertropical valuation theory, leaving aside nearly all proofs (to be found in [IKR1]). In this way we hope to give easy access to ideas of a new branch of so called…
We consider the group algebra of the symmetric group as a superalgebra, and describe its Lie subsuperalgebra generated by the transpositions. The updated version corrects some of the arguments made in Sections 4.5 - 4.7. The statements of…
The objective of this paper is to lay out the algebraic theory of supertropical vector spaces and linear algebra, utilizing the key antisymmetric relation of ``ghost surpasses.''Special attention is paid to the various notions of ``base,''…
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…
In this paper we investigate the problem of which Lie algebras appear as the derived algebra of a Lie algebra. We present new results that further develop this study and address two questions raised in a paper concerned with the…
The purpose of this paper is to generalize some results on $n$-Lie algebras and $n$-Hom-Lie algebras to $n$-Hom-Lie color algebras. Then we introduce and give some constructions of $n$-Hom-Lie color algebras.
This paper is the third in a series of papers, the aim of which is to construct algebraic geometry over metabelian Lie algebras.
The purpose of this paper is to continue the study of chief factors of a Lie algebra and to prove a further strengthening of the Jordan-H\"older Theorem for chief series.
We propose a notion of a super n-Lie algebra and construct a super n-Lie algebra with the help of a given binary super Lie algebra which is equipped with an analog of a supertrace. We apply this approach to the super Lie algebra of a…
We construct the Lie algebra of an n-Lie algebra and we also define the notion of cohomology of an n-Lie algebra.
We show that the Lie's Theorem holds for Lie color algebras with a torsion-free abelian group $G$. We give an example to show that the torsion-free condition is necessary.
In this paper, we attempt to develop the Schreier theory for two special types extensions of multiplicative Lie algebras.
In this paper we give an elementary proof of the Fundamental Theorem of Algebra for polynomials over the rational tropical semi-ring. We prove that, tropically, the rational numbers are algebraically closed. We provide a simple algorithm…
Generalizing supertropical algebras, we present a "layered" structure, "sorted" by a semiring which permits varying ghost layers, and indicate how it is more amenable than the "standard" supertropical construction in factorizations of…
Tropical mathematics is used to establish a correspondence between certain microscopic and macroscopic objects in statistical models. Tropical algebra gives a common framework for macrosystems (subsets) and their elementary constituents…
We consider the problem of constructing semisimple subalgebras of real (semi-) simple Lie algebras. We develop computational methods that help to deal with this problem. Our methods boil down to solving a set of polynomial equations. In…
We develop structure theory of finite Lie conformal superalgebras.
In this paper, the author gives two methods to construct complete Lie algebras. Both methods show that the derivation algebras of some Lie algebras are complete.