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On Locally Isomorphic Groups and Cartan-Stiefel Diagrams

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Symposia on Theoretical Physics and Mathematics

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Abstract

The groups considered in this review article are the semi-simple compact and connected Lie groups. Given such a group, all the (semisimple compact connected Lie) groups which are locally isomorphic to it are determined. The relations which hold among the members of such a set of groups—called a family—are given, i.e., the relations between a group, its covering groups, and its universal covering group are established.1,2 For the semisimple compact connected Lie groups, diagrams can be derived—the so called Cartan-Stiefel diagrams. The connections between these diagrams and the results stated for the families of locally isomorphic groups will be established in the second part of this article.3,4

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Author notes

  1. B. Gruber

    Present address: Dept. of Physics, St. Louis University, St. Louis, Mo., USA

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  1. Istituto Nazionale Di Fisica Nucleare, Sezione di Napoli, Italy

    B. Gruber

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  1. B. Gruber
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Alladi Ramakrishnan (Director of the Institute)

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© 1968 Springer Science+Business Media New York

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Gruber, B. (1968). On Locally Isomorphic Groups and Cartan-Stiefel Diagrams. In: Ramakrishnan, A. (eds) Symposia on Theoretical Physics and Mathematics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-5424-4_1

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  • DOI: https://doi.org/10.1007/978-1-4899-5424-4_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-5426-8

  • Online ISBN: 978-1-4899-5424-4

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