Talk:Quaternion algebra

Thank you!

Thank you so much for this outstanding and very important article on the concept of classical 19 century quaternion geometry from the point of view of modern algebra. It very greatly helps to clarify certain problems in nomenclature.

A link has been added from the word algebra to this outstanding article. Classical_Hamiltonian_quaternions#Contexts_of_Quaternion_Geometry_and_Linear_Algebra

Index two

Does anyone know what is an "element of index two" in a group? Thanks

An element whose order is half the order of the group itself? I'm not familiar with this terminology but an intuitive definition for "the index of an element" would be "the index of the subgroup generated by the element".Malatinszky (talk) 16:39, 27 February 2009 (UTC)

Here I think it should just read order 2. Charles Matthews (talk) 17:52, 27 February 2009 (UTC)

More explanation would be good

In the statement

"The norm form

$N(t+xi+yj+zk)=t^{2}-ax^{2}-by^{2}+abz^{2}\$

defines a structure of division algebra if and only if the norm is an anisotropic quadratic form, that is, zero only on the zero element."

it is not clear how the norm defines "defines a structure of [a] division algebra", and more explanation would be very helpful here. 2601:200:C000:1A0:90E6:F29F:F511:B9ED (talk) 18:48, 8 June 2021 (UTC)