On the tensor system of a semisimple Lie algebra

1972 ◽  
Vol 71 (2) ◽  
pp. 211-226 ◽  
Author(s):  
Timothy Murphy

AbstractFrom the tensorial point of view, the essential characteristic of a semisimple lie algebra A is the non-singularity of the Killing form, since this enables one to construct a system of Cartesian tensors over A. That system is the subject of this paper.

1974 ◽  
Vol 26 (3) ◽  
pp. 583-592 ◽  
Author(s):  
C. Y. Lee

An element in the centre of the universal enveloping algebra of a semisimple Lie algebra was first constructed by Casimir by means of the Killing form. By Schur's lemma, in an irreducible finite-dimensional representation elements in the centre are represented by diagonal matrices of all whose eigenvalues are equal. In section 2 of this paper, we show the existence of a complete set of generators whose eigenvalues in an irreducible representation are closely related to polynomial invariants of the Weyl group W of the Lie algebra (Theorem 1).


2001 ◽  
Vol 64 (1) ◽  
pp. 61-80 ◽  
Author(s):  
DMITRI I. PANYUSHEV

Let [hfr ] be a reductive subalgebra of a semisimple Lie algebra [gfr ] and C[hfr ] ∈ U([hfr ]) be the Casimir element determined by the restriction of the Killing form on [gfr ] to [hfr ]. The paper studies eigenvalues of C[hfr ] on the isotropy representation [mfr ]≃[gfr ]/[hfr ]. Some general estimates connecting the eigenvalues and the Dynkin indices of [mfr ] are given. If [hfr ] is a symmetric subalgebra, it is shown that describing the maximal eigenvalue of C[hfr ] on exterior powers of [mfr ] is connected with possible dimensions of commutative Lie subalgebras in [mfr ], thereby extending a result of Kostant. In this situation, a formula is also given for the maximal eigenvalue of C[hfr ] on ∧ [mfr ]. More generally, a similar picture arises if [hfr ] = [gfr ]Θ, where Θ is an automorphism of finite order m and [mfr ] is replaced by the eigenspace of Θ corresponding to a primitive mth root of unity.


2021 ◽  
Vol 7 (1) ◽  
pp. 43-49
Author(s):  
Anoh Yannick Kraidi ◽  
Kinvi Kangni

AbstractLet 𝔤 be a semisimple Lie algebra, j a Cartan subalgebra of 𝔤, j*, the dual of j, jv the bidual of j and B(., .) the restriction to j of the Killing form of 𝔤. In this work, we will construct a chain of reproducing kernel Cartan subalgebras ordered by inclusion.


1976 ◽  
Vol 15 (05) ◽  
pp. 246-247
Author(s):  
S. C. Jain ◽  
G. C. Bhola ◽  
A. Nagaratnam ◽  
M. M. Gupta

SummaryIn the Marinelli chair, a geometry widely used in whole body counting, the lower part of the leg is seen quite inefficiently by the detector. The present paper describes an attempt to modify the standard chair geometry to minimise this limitation. The subject sits crossed-legged in the “Buddha Posture” in the standard chair. Studies with humanoid phantoms and a volunteer sitting in the Buddha posture show that this modification brings marked improvement over the Marinelli chair both from the point of view of sensitivity and uniformity of spatial response.


2003 ◽  
Vol 42 (2) ◽  
pp. 170-172
Author(s):  
Mir Annice Mahmood

To implement any successful policy, research about the subject-matter is essential. Lack of knowledge would result in failure and, from an economic point of view, it would lead to a waste of scarce resources. The book under review is essentially a manual which highlights the use of research for development. The book is divided into two parts. Part One informs the reader about concepts and some theory, and Part Two deals with the issue of undertaking research for development. Both parts have 11 chapters each. Chapter 1 asks the basic question: Is research important in development work? The answer is that it is. Research has many dimensions: from the basic asking of questions to the more sophisticated broad-based analysis of policy issues. The chapter, in short, stresses the usefulness of research which development workers ignore at their own peril.


2015 ◽  
Vol 10 (3) ◽  
pp. 275-289
Author(s):  
Tadeusz Liziński ◽  
Marcin Bukowski ◽  
Anna Wróblewska

Projects for flood protection are increasingly the subject of investment projects in the field of water management. This is related to the increasing frequency of worldwide threats caused by extreme weather conditions, including extremely high rainfall causing floods. Technical and nontechnical flood protection measures are also increasing in importance. In the decision-making process, it is necessary to take into account both the costs and benefits of avoiding losses, including an analysis of social benefits, whose valuation of non-market goods is an essential element. A comprehensive account of projects in the field of flood protection based on the estimated costs and benefits of the investment allows the economic efficiency from a general social point of view to be determined. Previous evaluations of the effectiveness of investment projects have mainly taken into account only categories and market values. The aim of the article is to identify the possibilities to expand the values of non-market assessments and categories formulated on the basis of the theoretical economics of the environment. 


2020 ◽  
Vol 15 (1-3) ◽  
pp. 44-59
Author(s):  
Lidia Peneva

Crimes against marriage and family are a particular group of social relation­ships that the law has defended properly in view of the high public significance and value they enjoy. At the moment they are regulated in Chapter VI, Section I, of the specific part of the Penal Code the Repub­lic of Bulgaria. The subject matter of this Statement will, however, be the legisla­tive provisions concerning these criminal­ized acts in retrospect. The purpose of the study is to show by historical method and through the comparatively legal method the development of these criminal groups during the periods of various criminal laws in Bulgaria. This will also provide a basis for reflection on possible de lege ferenda proposals. This report from a structural point of view will be divided into three distinct points, marking each of the penal laws in the Republic of Bulgaria, which were in force before 1968.


Author(s):  
Yu.V. Kupriyanova ◽  
I.M. Vasilyanova

The article summarizes the key points in the development of the metadialogue phenomenon from a linguistic point of view. Some stages of the development of this concept and the difficulties associated with its structuring are covered. The main research findings of modern foreign and domestic experts on its study are considered. Some characteristics of the subject of the research from the standpoint of various pragmatic installations are given. On the basis of the dynamic structure of the metadialogue development, certain principles of semantic relations connected with the dialectical nature of human cognition are presented. Excursion into the history and evolution of the concept is presented. Several types of formulation of the subject matter are given. In accordance with the goal of speech exposure, internal problems of the development of metadialogue are highlighted and the critical points related to solving these problems are described. The rules of metadialogue flow are explained at the level of steps, the success/failure of which directly affects the final result of communication. The prospects of development of the concept research in accordance with various types of discourse are indicated.


1992 ◽  
Vol 9 (2) ◽  
pp. 202-218 ◽  
Author(s):  
M. Ramzan Akhtar

IntroductionIslamic teachings envisage a balanced society achieved through thefunctioning of Islamic institutions. This paper visualizes three main institutions:ukhiwah, ‘adl, and ihsan. Ukhuwah (brotherhood) promotes the bonds ofbrotherhood, and ‘adl (justice) enforces a system of individual and socialobligations. Islam stresses the importance of meeting one’s obligations, becauseeach obligation has its corresponding right. Thus, an individual’s effort to meethidher obligations leads to the fulfillment of everyone’s rights. This does notmean that Islam forbids one from demanding hidher rights, even though thisdemand does pose a problem related to human nature: an individual wants his/herrights and also some part of another person’s rights. Therefore, one group’sdemand for its rights tends to encroach upon the rights of another group, whichcauses social friction and disorder. The institution of ihsan (benevolence) goesone step further: it exhorts individuals to forego their rights for the sake of others,which is considered an act of piety.This paper will study employer-employee relationships in the light of thethree institutions mentioned above. A framework for conducting employer-employeerelationships is formulated and is then used to determine, from theIslamic point of view, the proper wages. The findings of this paper show thatan economically efficient and equitable wage structure can evolve within thisframework and that such a wage structure would promote the parties’ mutualrelationships which, in turn, would lead to industrial peace.The body of the paper is organized as follows: a review of the existingliterature on the subject, the development of an Islamic framework for employer-employeerelationships, a discussion of the Islamic approach to wagecompensation, and some concluding remarks ...


2015 ◽  
Vol 5 (2) ◽  
pp. 148-171
Author(s):  
Denisa Gunišová ◽  
Jana Duchovičová

Authors in this contribution focus on issue of subject matter structure creation by the teacher as an important psycho-didactic domain of education process and how does a student perceive this structure. The aim of the teacher is not only to impart the knowledge to students but also to show them and teach them possible ways of how to understand the subject matter better and how to get to the fundamentals of it. Based on the structure of subject matter created by the teacher a student creates cognitive frames which become basis for his further learning. We pay attention to definition of epistemology of subject matter structure, questions of psycho-didactic approach to teaching, creating structure of subject matter and how does the teacher work with the text. Empirical part of the contribution investigates teachers' preferences of subject matter structure and statistically describes subjective perception of level of understanding of the subject matter by a student influenced by the particular subject matter structure realized by the teacher.


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