Abstract
It is shown that every finitely generated continuous group has a subgroup generated by its infinitesimal transformations. This subgroup has a group algebra which is the Lie algebra of the group. By obtaining complete systems in the Lie algebra and complete rectangular arrays, it is shown that these can yield matrix representations of the continuous group. Illustrative examples are given for the rotation groups and for the full linear groups. It would seem that all the finite motion representations can be obtained by these methods, including spin representations of rotation groups. But the completeness of the method is not here demonstrated.
Similar content being viewed by others
References
Dodds, B. (1973).Annali di Matematica,95, 243–254.
Joos, H. (1959). “Bemerkungen zur Phase-Shift Analysis auf Grund der Darstellungstheorie der inhomogen Lorentz Gruppe” Oberwolfach (unpublished).
Littlewood, D. E. (1958).A University Algebra, (2nd ed.) Heinemann.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Littlewood, D.E. Lie algebras and representations of continuous groups. Int J Theor Phys 14, 97–109 (1975). https://doi.org/10.1007/BF01807978
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01807978