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| In ], the '''trigintaduonions''' (from the Latin ''trigintaduo'' meaning 32) form a 32-] ] over the ].<ref>, University of Waterloo</ref> They are constructed from the ]s by applying the ].<ref name=cawgas>, Raoul E. Cawgas and co-authors</ref> | In ], the '''trigintaduonions''' (from the Latin ''trigintaduo'' meaning 32) form a 32-] ] over the ].<ref>, University of Waterloo</ref> They are constructed from the ]s by applying the ].<ref name=cawgas>, Raoul E. Cawgas and co-authors</ref> | ||
Revision as of 21:31, 21 December 2009
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In abstract algebra, the trigintaduonions (from the Latin trigintaduo meaning 32) form a 32-dimensional algebra over the reals. They are constructed from the sedenions by applying the Cayley–Dickson construction.
Like the sedenions, which they contain as a sub-algebra, trigintaduonions are neither commutative, associative nor alternative. They do preserve the property of being power associative.
References
- C++ Complex Numbers, Quaternions, Octonions, Sedenions, etc., University of Waterloo
- ^ The Basic Subalgebra Structure of the Cayley-Dickson Algebra of Dimension 32 (Trigintaduonions), Raoul E. Cawgas and co-authors
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