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Generalizations of Lie Groups

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Book cover Lie Groups and Lie Algebras I

Part of the book series: Encyclopaedia of Mathematical Sciences ((EMS,volume 20))

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Abstract

This chapter contains a brief survey of certain theories generalizing the classical Lie theory. This survey does not aspire to completeness. In particular, we do not touch on the theory of algebraic groups and topological groups are considered only in connection with Hilbert’s 5th problem. These subjects, naturally, require separate surveys. The same can be said about “infinite” continuous groups (or Lie pseudo-groups), the study of which was originated already by S. Lie. Beyond the scope of this survey remain the Kac-Moody algebras and the groups corresponding to them, as well as Lie supergroups and superalgebras.

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  1. Yaroslavl University, Sovetskaya ul. 14, 150000, Yaroslavl, Russia

    A. L. Onishchik

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    A. L. Onishchik

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Onishchik, A.L. (1993). Generalizations of Lie Groups. In: Onishchik, A.L. (eds) Lie Groups and Lie Algebras I. Encyclopaedia of Mathematical Sciences, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57999-8_5

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  • DOI: https://doi.org/10.1007/978-3-642-57999-8_5

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