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Co-actions of groups

Published online by Cambridge University Press:  11 July 2007

Martin Arkowitz  and
Mauricio Gutierrez
Martin Arkowitz
Affiliation:
Department of Mathematics, Dartmouth College, Hanover, NH 03755, USA (martin.arkowitz@dartmouth.edu)
Mauricio Gutierrez
Affiliation:
Department of Mathematics, Tufts University, Medford, MA 02155, USA (mgutierr@tufts.edu)
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Abstract

Let f : G → H be a fixed homomorphism and p′ : G * H → G and p″ : G * H → H the two projections of the free product. Then a co-action relative to f is a homomorphism s : G → G * H such that p′s = id and p″s = f. We study this notion and investigate the following questions. What restrictions does s place on the structure of the group G? What form does s take in special cases? When does s induce a co-multiplication on H? What is the relation between associativity of s and associativity of the induced co-multiplication m on H? What are the properties of the operation of Hom(H, B) on Hom(G, B) induced by s : G → G * H? In addition, we give several diverse examples of co-actions in the last section.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 2 , April 2001 , pp. 225 - 239
Copyright
Copyright © Royal Society of Edinburgh 2001

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