RESCINDED: Quaternion Series as a Division Algebra
373 views · Published 9 September 2018 · 24:01 · Indexed 18 October 2026
Channel: Doug Sweetser · 2018 · Science & Technology
Quaternion series are NOT a division algebra. Instead, quaternion series ARE a semigroup with inverses. I was aware these is more than one inverse for multiplication. That makes it a semigroup. Original description: A white board talk is presented to first define what a quaternion series is - a totally ordered array of quaternions with a row and column values defined such that rows * columns = the length of the array. To be a division algebra, both addition and multiplication must be group operations. That in turn involves showing four things: identity, inverse, closure, and associativity. [There are 2^n inverses, not one, which makes this a semigroup, not a division algebra.] A Jupyter notebook to accompany this notebook is available here: https://github.com/dougsweetser/QM/blob/master/docs/quaternion_series_division_algebra.ipynb
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