Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Multiplicative properties of power maps. II

Author: C. A. McGibbon
Journal: Trans. Amer. Math. Soc. 274 (1982), 479-508
MSC: Primary 55P45; Secondary 22E20
MathSciNet review: 675065
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The notions of $ A_n$-maps and $ C_n$-forms can be regarded as crude approximations to the concepts of homomorphisms and commutativity, respectively. These approximations are used to study power maps on connected Lie groups and their localizations. For such groups the power map $ x \mapsto {x^n}$ is known to be an $ A_2$-map if and only if $ n$ is a solution to a certain quadratic congruence. In this paper, $ A_3$-power maps are studied. For the Lie group Sp(l) it is shown that the $ A_3$-powers coincide with solutions which are common to the quadratic congruence, mentioned earlier, and another cubic congruence. Other Lie groups, when localized so as to become homotopy commutative, are also shown to have infinitely many $ A_3$-powers. The proofs reflect the combinatorial nature of the obstructions involved.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 55P45, 22E20

Retrieve articles in all journals with MSC: 55P45, 22E20

Additional Information

Keywords: $ A_n$-map, $ C_n$-form, projective $ n$-space, localization of spaces, homotopy commutativity
Article copyright: © Copyright 1982 American Mathematical Society