scholarly journals Finite-dimensional Leibniz algebra representations of $\mathfrak{sl}_2$

2021 ◽  
Author(s):  
Tuuelbay KURBANBAEV ◽  
Rustam TURDİBAEV
Keyword(s):  
Leibniz Algebra ◽  
Finite Dimensional

scholarly journals Varieties of Null-Filiform Leibniz Algebras Under the Action of Hopf Algebras

2021 ◽  
Author(s):  
Lucio Centrone ◽  
Chia Zargeh
Keyword(s):  
Hopf Algebra ◽  
Free Algebra ◽  
Hopf Algebras ◽  
Leibniz Algebra ◽  
Module Structure ◽  
Leibniz Algebras ◽  
Finite Dimensional ◽  
Filiform Leibniz Algebra ◽  
Algebra Over A Field ◽  
Cocommutative Hopf Algebra

AbstractLet L be an n-dimensional null-filiform Leibniz algebra over a field K. We consider a finite dimensional cocommutative Hopf algebra or a Taft algebra H and we describe the H-actions on L. Moreover we provide the set of H-identities and the description of the Sn-module structure of the relatively free algebra of L.

Finite-dimensional Leibniz algebras and combinatorial structures

2017 ◽  
Vol 20 (01) ◽  
pp. 1750004 ◽  
Author(s):  
M. Ceballos ◽  
J. Núñez ◽  
Á. F. Tenorio
Keyword(s):  
Leibniz Algebra ◽  
Combinatorial Structure ◽  
Combinatorial Structures ◽  
Leibniz Algebras ◽  
Finite Dimensional ◽  
Dimension 2

Given a finite-dimensional Leibniz algebra with certain basis, we show how to associate such algebra with a combinatorial structure of dimension 2. In some particular cases, this structure can be reduced to a digraph or a pseudodigraph. In this paper, we study some theoretical properties about this association and we determine the type of Leibniz algebra associated to each of them.

scholarly journals Leibniz algebras: a brief review of current results

2019 ◽  
Vol 11 (2) ◽  
pp. 250-257
Author(s):  
V.A. Chupordia ◽  
A.A. Pypka ◽  
N.N. Semko ◽  
V.S. Yashchuk
Keyword(s):  
Leibniz Algebra ◽  
Infinite Dimensional ◽  
Binary Operations ◽  
Leibniz Algebras ◽  
Finite Dimensional ◽  
Algebra Over A Field

Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[\cdot,\cdot]$. Then $L$ is called a left Leibniz algebra if it satisfies the left Leibniz identity $[[a,b],c]=[a,[b,c]]-[b,[a, c]]$ for all $a,b,c\in L$. This paper is a brief review of some current results, which related to finite-dimensional and infinite-dimensional Leibniz algebras.

scholarly journals Some Leibniz bimodules of 𝔰𝔩2

2019 ◽  
Vol 19 (04) ◽  
pp. 2050064 ◽  
Author(s):  
T. Kurbanbaev ◽  
R. Turdibaev
Keyword(s):  
Lie Algebra ◽  
Simple Formula ◽  
Leibniz Algebra ◽  
Direct Sum ◽  
Finite Dimensional ◽  
Leibniz Formula ◽  
Algebra Module

We study complex finite-dimensional Leibniz algebra bimodule over [Formula: see text] that as a Lie algebra module is split into a direct sum of two simple [Formula: see text]-modules. We prove that in this case there are only two nonsplit Leibniz [Formula: see text]-bimodules and we describe the actions.

Non-Linear Dynamics of Cardiovascular Variability Signals

1994 ◽  
Vol 33 (01) ◽  
pp. 81-84 ◽  
Author(s):  
S. Cerutti ◽  
S. Guzzetti ◽  
R. Parola ◽  
M.G. Signorini
Keyword(s):  
Dimensional Space ◽  
Severe Heart Failure ◽  
Parametric Models ◽  
Deterministic Systems ◽  
Finite Dimensional ◽  
Return Maps ◽  
Pathological Conditions ◽  
Non Linear ◽  
Space State

Abstract:Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heart failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

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