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BOUNDS ON THE LEVELS OF COMPOSITION ALGEBRAS
Mathematical Proceedings of the Royal Irish Academy
Vol. 110A, No. 1 (AUGUST 2010), pp. 21-30
Published by: Royal Irish Academy
Stable URL: http://www.jstor.org/stable/25767131
Page Count: 10
You can always find the topics here!Topics: Quaternion algebra, Algebra, Mathematical theorems, Quaternions, Abstract algebra, Isotropy, Integers, Value theorems, Mathematics
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Certain families of quaternion and octonion algebras are conjectured to be of level and sublevel n. A proof of this conjecture is offered in the case where n is a power of two. Hoffmann's proof of the existence of infinitely many new values for the level of a quaternion algebra is generalised and adapted. Alternative constructions of quaternion and octonion algebras are introduced and justified in the case where n is a multiple of a two power.
Mathematical Proceedings of the Royal Irish Academy © 2010 Royal Irish Academy