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On Curtis' theorem about finite octonionic loops
Author(s):
Paul
Boddington;
Dmitriy
Rumynin
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1651-1657.
MSC (2000):
Primary 17D05;
Secondary 17B20
Posted:
January 9, 2007
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Abstract:
We prove a stronger version of Curtis' classification theorem of finite subloops of the Cayley octonions  .
References:
-
- 1.
- C. Jordan, Memoire sur les equations differentielles lineaires a integrale algebrique, J. Reine Angew. Math., 84 (1878), 89-215.
- 2.
- J. McKay, Graphs, singularities, and finite groups, in Santa Cruz conference on finite groups, Proc. Symp. Pure Math. 37, 1980, pp 183-186.MR 0604577 (82e:20014)
- 3.
- R. T. Curtis, A classification and investigation of the finite subloops of the Cayley-Dickson algebra, manuscript, 1970.
- 4.
- R. T. Curtis, Construction of a family of Moufang loops, Math. Proc. Cambridge Philos. Soc., to appear.
- 5.
- Y. Ito, I. Nakamura, Hilbert schemes and simple singularities. New trends in algebraic geometry (Warwick, 1996), 151-233, Cambridge University Press, Cambridge, 1999.MR 1714824 (2000i:14004)
- 6.
- J. Humphreys, Reflection Groups and Coxeter Groups. Cambridge University Press, Cambridge, 1990.MR 1066460 (92h:20002)
- 7.
- J. Conway, D. Smith, On quaternions and octonions: their geometry, arithmetic, and symmetry. A K Peters, Natick, 2003. MR 1957212 (2004a:17002)
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Additional Information:
Paul
Boddington
Affiliation:
Department of Mathematics, University of Warwick, Coventry, CV4 7AL, United Kingdom
Email:
paulsboddington@yahoo.co.uk
Dmitriy
Rumynin
Affiliation:
Department of Mathematics, University of Warwick, Coventry, CV4 7AL, United Kingdom
Email:
rumynin@maths.warwick.ac.uk
DOI:
10.1090/S0002-9939-07-08707-2
PII:
S 0002-9939(07)08707-2
Keywords:
Octonions,
quaternions,
loop,
root system
Received by editor(s):
July 19, 2005
Received by editor(s) in revised form:
February 24, 2006
Posted:
January 9, 2007
Communicated by:
Jonathan I. Hall
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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