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Applications of isotopy to real division algebras

Conference · · Hadronic J.; (United States)
OSTI ID:6693081
In this paper we illustrate how the notion of isotopy can be used to solve various problems concerning finite-dimensional division algebras over the real numbers. In particular, we show that the 8-dimensional division algebras which have the same derivation algebra as the octonions, and hence which most resemble the octonions, are not in general isotopes of the octonions. Secondly, using a result of Hopf, we argue that every commutative division algebra is the reals or is isomorphic to a special kind of isotope of the complex numbers. Finally, by considering a certain class of algebras, we show how isotopy is a useful tool for determining necessary and sufficient conditions on the multiplication constants in order to have a division algebra.
OSTI ID:
6693081
Report Number(s):
CONF-8008162-
Conference Information:
Journal Name: Hadronic J.; (United States) Journal Volume: 4:2
Country of Publication:
United States
Language:
English

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