On the exponential of the 2-forms in relativity
type: Item
instance of: scholarly article
title: On the exponential of the 2-forms in relativity
zbMATH Open document ID: 0708.53025
DOI: 10.1007/BF00764159
author: Bartolomé Coll
author: Fernando San José
published in: General Relativity and Gravitation
publication date: 1990-01-01T00:00:00Z
review text: The reviewer was somewhat puzzled by this paper. Its intentions were to give a discussion of the Lorentz group through the exponential process applied to bivectors (2-forms) and, indeed, it seems to do this in a thorough way. However, as far as the reviewer can see, much of the material in the paper is known, often in a simpler and more convenient form [see the papers of \textit{R. Shaw} in Q. J. Math., Oxf. II. Ser. 20, 333-345 (1969; Zbl 0181.282); ibid. 21, 101-124 (1970; Zbl 0217.087), and by \textit{R. Shaw} and \textit{G. Bowtell}, ibid. 20, 497-503 (1969)]. The paper, somewhat unusually, contains no bibliography. Amongst the topics treated in the paper are the classification of Lorentz transformations and the same transformations achieved by exponentiation of bivectors. However, the classification of Lorentz transformations by means of Jordan matrix theory and their minimal and characteristic polynomial structure can be found in the above papers of Shaw whilst the method of exponentiating the members of the Lie algebra of the Lorentz group (which consists of skew self-adjoint matrices - essentially bivectors) is well known and, together with the bivector logarithm, is also treated in Shaw's papers. The reviewer also found the abstract and introduction somewhat puzzling - in particular it does not appear to be relevant in the study of Lie algebras of Killing vector fields on space- time. In spite of this criticism the paper is still an interesting read and approaches the problem from a different angle. It is certainly well written.
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 83C99
Mathematics Subject Classification ID: 53B50
zbMATH DE Number: 4163654
zbMATH Keywords: exponentiation
zbMATH Keywords: symmetry
zbMATH Keywords: Lorentz group
zbMATH Keywords: bivectors
reviewed by: G. S. Hall
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4163654