Submission: 2007, Feb 20
Constructions of quaternion and octonion algebras, suggested to have new level and sublevel values, are proposed and justified. In particular, octonion algebras of level and sublevel 6 and 7 are constructed. In addition, Hoffmann's proof of the existence of infinitely many new values for the level of a quaternion algebra is generalised and adapted.
2000 Mathematics Subject Classification: Primary 11E04; Secondary 11E25, 17A75, 16K20
Keywords and Phrases: Quaternion algebra, octonion algebra, level, sublevel, function field of a quadratic form
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