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On Anti-Commutative Algebras and Analytic Loops

Published online by Cambridge University Press:  20 November 2018

Arthur A. Sagle
Arthur A. Sagle*
Affiliation:
University of California, Los Angeles
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In (4) Malcev generalizes the notion of the Lie algebra of a Lie group to that of an anti-commutative "tangent algebra" of an analytic loop. In this paper we shall discuss these concepts briefly and modify them to the situation where the cancellation laws in the loop are replaced by a unique two-sided inverse. Thus we shall have a set H with a binary operation xy defined on it having the algebraic properties

(1.1) H contains a two-sided identity element e;

(1.2) for every x ∊ H, there exists a unique element x-1 ∊ H such that xx-1 = x-1x = e;

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 550 - 558
Copyright
Copyright © Canadian Mathematical Society 1965

References

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