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Generalized Fuzzy lie Ideals of lie algebras

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模糊系统与数学 2010年第4期24卷 48-55页

作者： M.Akram B.Davvaz K.P.Shum Punjab University College of Information Technology University of the PunjabOld Campus Department of Mathematics Yazd University Department of Mathematics The University of Hong Kong

In this paper we introduce new generalized fuzzy lie ideals of lie algebras and study some of their important *** characterize these generalized lie ideals of lie algebras by their level *** characterization of the ge... 详细信息

关键词： lie algebras (∈,∈∨q)-fuzzy lie Ideals lie Ideals with Thresholds

Single-Valued Neutrosophic lie algebras

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Journal of Mathematical Research with Applications 2019年第2期39卷 141-152页

作者： Muhammad AKRAM Hina GULZAR Kar Ping SHUM Department of Mathematics University of the Punjab New Campus Institute of Mathematics Yunnan University

A single-valued neutrosophic(SVN) set is a powerful general formal framework that generalizes the concept of fuzzy set and intuitionistic fuzzy set. In SVN set, indeterminacy is quantified explicitly, and truth membership, indeterminacy membership, and falsity membership are independent. In this paper, we apply the notion of SVN sets to lie algebras. We develop the concepts of SVN lie subalgebras and SVN lie ideals. We describe some interesting results of SVN lie ideals.

关键词： Single-valued neutrosophic sets lie ideals lie algebras

Root Systems lie algebras

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Advances in Linear Algebra & Matrix Theory 2023年第1期13卷 1-20页

作者： Amor Hasić Fatih Destović Department of Computer Science International University of Novi Pazar Novi Pazar Serbia Faculty of Educational Sciences University of Sarajevo Sarajevo Bosnia and Herzegovina

A root system is any collection of vectors that has properties that satisfy the roots of a semi simple lie algebra. If g is semi simple, then the root system A, (Q) can be described as a system of vectors in a Euclidean vector space that possesses some remarkable symmetries and completely defines the lie algebra of g. The purpose of this paper is to show the essentiality of the root system on the lie algebra. In addition, the paper will mention the connection between the root system and Ways chambers. In addition, we will show Dynkin diagrams, which are an integral part of the root system.

关键词： lie algebras Root Systems Ways Chambers Dynkin Diagrams

Dictionary on lie algebras and superalgebras

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A Specialization of Prinjective Ringel-Hall Algebra and the associated lie algebra

2000年

作者： Luc Frappat Antonino Sciarrino Paul Sorba

ISBN: (纸本)0122653408;9780122653407

This book is a detailed reference on lie algebras and lie superalgebras presented in the form of a dictionary. It is intended to be useful to mathematical and theoretical physicists, from the level of the graduate student upwards. The Dictionary will serve as the reference of choice for practitioners and students alike. Key Features:* Compiles and presents material currently scattered throughout numerous textbooks and specialist journal articles* Dictionary format provides an easy to use reference on the essential topics concerning lie algebras and lie superalgebras* Covers the structure of lie algebras and lie superalgebras and their finite dimensional representation theory* Includes numerous tables of the properties of individual lie algebras and lie superalgebras

关键词： lie algebras

来源：畅想之星图书光盘版（南... 评论

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Acta Mathematica Sinica,English Series 2008年第10期24卷 1687-1702页

作者： Justyna KOSAKOWSKA Faculty of Mathematics and Computer Science Nicolaus Copernicus Universityul. Chopina 12//18 87-100 Toru■ Poland

In the present paper we describe a specialization of prinjective Ringel-Hall algebra to 1, for prinjective modules over incidence algebras of posets of finite prinjective type, by generators and relations. This gives us a generalisation of Serre relations for semisimple lie algebras. Connections of prinjective Ringel-Hall algebras with classical lie algebras are also discussed.

关键词： Ringel-Hall algebras lie algebras prinjective modules poset representations

A Few Expanding Integrable Models, Hamiltonian Structures and Constrained Flows

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Communications in Theoretical Physics 2011年第2期55卷 273-290页

作者：张玉峰 College of Science China University of Mining and Technology

Two kinds of higher-dimensional lie algebras and their loop algebras are introduced, for which a few expanding integrable models including the coupling integrable couplings of the Broer-Kaup （BK） hierarchy and the dispersive long wave （DLW） hierarchy as well as the TB hierarchy are obtained. From the reductions of the coupling integrable couplings, the corresponding coupled integrable couplings of the BK equation, the DLW equation, and the TB equation are obtained, respectively. Especiaily, the coupling integrable coupling of the TB equation reduces to a few integrable couplings of the well-known mKdV equation. The Hamiltonian structures of the coupling integrable couplings of the three kinds of soliton hierarchies are worked out, respectively, by employing the variationai identity. Finally, we decompose the BK hierarchy of evolution equations into x-constrained flows and tn-eonstrained flows whose adjoint representations and the Lax pairs are given.

关键词： lie algebras Broer-Kaup hierarchy dispersive long wave hierarchy constrained flow

Coherent States for the Two-Dimensional Dirac-Moshinsky Oscillator Coupled to an External Magnetic Field

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Communications in Theoretical Physics 2015年第3期63卷 271-274页

作者： D.Ojeda-Guillen R.D.Mota V.D.Granados Escuela Superior de Física y Matemáticas Instituto Politécnico NacionalEd.9Unidad Profesional Adolfo López MateosC.P.07738México D.F.Mexico Escuela Superior de Ingeniería Mecánica y Eléctrica Unidad CulhuacánInstituto Politécnico NacionalAv.Santa Ana No.1000Col.San Francisco CulhuacánDelegación CoyoacánC.P.04430Mexico D.F.Mexico

We show that the（2＋1）-dimensional Dirac-Moshinsky oscillator coupled to an externa/ magnetic field can be treated algebraically with the SU（1,1） group theory and its group *** use the su（1,1） irreducible representation theory to find the energy spectrum and the ***,with the su（1,1） group basis we construct the relativistic coherent states in a closed form for this problem.

关键词： lie algebras coherent states Dirac equation Dirac-Moshinsky oscillator

Geometry Algorisms of Dynkin Diagrams in lie Group Machine Learning

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南昌工程学院学报 2006年第2期25卷 74-78页

作者： Huan Xu Fanzhang Li Computer Science ＆ Technology School Soochow University Suzhou 215006 China

This paper uses the geometric method to describe lie group machine learning(LML)based on the theoretical framework of LML,which gives the geometric algorithms of Dynkin diagrams in *** includes the basic conceptions of Dynkin diagrams in LML,the classification theorems of Dynkin diagrams in LML,the classification algorithm of Dynkin diagrams in LML and the verification of the classification algorithm with experimental results.

关键词： lie group machine learning Dynkin diagrams lie algebras