Applications of isotopy to real division algebras
- Univ. of Wisconsin, Madison
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-
- Journal Information:
- Hadronic J.; (United States), Vol. 4:2; Conference: 3. workshop on Lie-admissible formulations, Boston, MA, USA, 4 Aug 1980
- Country of Publication:
- United States
- Language:
- English
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