Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Added these pointers:
Daniel K. Biss, Daniel Dugger, Daniel Isaksen, Large annihilators in Cayley-Dickson algebras, Communications in Algebra 36 (2), 632-664, 2008 (arxiv:math/0511691)
Daniel K. Biss, Daniel Christensen, Daniel Dugger, Daniel Isaksen, Large annihilators in Cayley-Dickson algebras II, Boletin de la Sociedad Matematica Mexicana (3) 13(2) (2007), 269-292 (arxiv:math/0702075)
Daniel K. Biss, Daniel Christensen, Daniel Dugger, Daniel Isaksen, Eigentheory of Cayley-Dickson algebras, Forum Mathematicum 21(5) (2009), 833-851 (arxiv:0905.2987)
added pointer to the original article:
For the record and for my peace of mind, I have spelled out in full detail the computation which shows the equivalence between the component formula
$(a,b) (c, d) \;\coloneqq\; (a c - d \overline{b}, \overline{a} d + c b)$and the relations
$a (\ell b) = \ell (\overline{a} b) \,, \phantom{AA} (a \ell) b = (a \overline{b}) \ell \,, \phantom{AA} (\ell a) (b \ell) = - \overline{a b}$As it goes, this showed that the previous version of the entry was wrong: There are two versions of the component formula, depending on whether one identifies
$(a,b) \leftrightarrow a + \ell b$or
$(a,b) \leftrightarrow a + b \ell$and the previous version wasn’t consistent about this across subsections.
I have now changed everything to the first version. For completeness one should eventually add at least a remark about the second version.
Who is the first to state the minimal set of relation
$a (\ell b) = \ell (\overline{a} b) \,, \phantom{AA} (a \ell) b = (a \overline{b}) \ell \,, \phantom{AA} (\ell a) (b \ell) = - \overline{a b}$?
Around (6) of Dickson 1919 the idea of generators $i, j, k , \ell$ appears, but not this minimal choice of set of relations.
Is this original to Baez 02, where it appears in the second half of section 2.2?
1 to 6 of 6