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August 20

Name for a particular type of hypercomplex number

Is there a name for the associative and commutative four-dimensional algebra over R (the real numbers) that is the Klein four-group R-algebra, R[V]? It is a kind of hypercomplex number with a multiplication table that is like that of the quaternions and bicomplex numbers, except with all minus signs removed, as in Dimensional analysis#Siano's extension: orientational analysis. Also defined by i² = j² = k² = ijk = +1. It also may be defined as the direct sum of rings R⊕R⊕R⊕R. — Quondum 22:18, 20 August 2013 (UTC)[reply]