Classification And Identification Of Lie Algebras
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Classification and Identification of Lie Algebras
Author: Libor Šnob
language: en
Publisher: American Mathematical Soc.
Release Date: 2017-04-05
The purpose of this book is to serve as a tool for researchers and practitioners who apply Lie algebras and Lie groups to solve problems arising in science and engineering. The authors address the problem of expressing a Lie algebra obtained in some arbitrary basis in a more suitable basis in which all essential features of the Lie algebra are directly visible. This includes algorithms accomplishing decomposition into a direct sum, identification of the radical and the Levi decomposition, and the computation of the nilradical and of the Casimir invariants. Examples are given for each algorithm. For low-dimensional Lie algebras this makes it possible to identify the given Lie algebra completely. The authors provide a representative list of all Lie algebras of dimension less or equal to 6 together with their important properties, including their Casimir invariants. The list is ordered in a way to make identification easy, using only basis independent properties of the Lie algebras. They also describe certain classes of nilpotent and solvable Lie algebras of arbitrary finite dimensions for which complete or partial classification exists and discuss in detail their construction and properties. The book is based on material that was previously dispersed in journal articles, many of them written by one or both of the authors together with their collaborators. The reader of this book should be familiar with Lie algebra theory at an introductory level.
On Einstein’s Path
Author: Alex Harvey
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Friends and colleagues of Engelbert Schucking came together in a symposium on the 12th and 13th of December 1996 at New York University to celebrate and express to him their respect, admiration, and affection. They came to celebrate his scientific and scholarly achievements, the inspirational quality of his teaching, his graciousness as a colleague, his thoughtful guidance of graduate students, his service to the department, the university and the physics community at large-and, not least, his open, courteous, easy accessibility to anyone needing his counselor expertise. The announcement was A SYMPOSIUM In Honor of PROF. ENGELBERT SCHUCKING Physics Department-New York University On December 12th and 13th there will be a Symposium to honor Professor Engel bert Schucking for his service to the University, the Department, and the Physics Community. The December 12th session will run from 1 to 6 PM followed by a reception. The following morning the session will run from 9 AM to 1 PM. Atten dance (including the reception) is open to all friends and colleagues of Professor Schucking and anyone interested in General Relativity. The talks will be presented in Room 121, 4 Washington Place; the reception will be in the office of Dean Furmankis, 5 Washington Square North from 6:15 to 8:00 PM Thursday Afternoon: Greetings Alice S.
Discrete, Finite and Lie Groups
Author: Pietro Giuseppe Fré
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2023-08-07
In a self contained and exhaustive work the author covers Group Theory in its multifaceted aspects, treating its conceptual foundations in a proper logical order. First discrete and finite group theory, that includes the entire chemical-physical field of crystallography is developed self consistently, followed by the structural theory of Lie Algebras with a complete exposition of the roots and Dynkin diagrams lore. A primary on Fibre-Bundles, Connections and Gauge fields, Riemannian Geometry and the theory of Homogeneous Spaces G/H is also included and systematically developed. https://petrusfremathandlit.net