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" tommy quaternion "
#4
Hi, why you don't specify that in your list of identities? You forgot to add it or it is possible to derive it from the others?

Also, you see it as a non-associative algebra over the reals or the complex?

Trivial question (sorry but I'm new to linear algebra): being an algebra means that is a -vector space of dimension d=4 on which is defined a bilinear application that is not associative... but it must be bilinear because we want it distributive:

  1. An element is of the form . Let  , the application being distributive means that



    i.e. every translation by a Tommy quaternion is a endomorphism of  the addition group;


  2. and we also want that for every scalar



    i.e we want it to contain a copy of the base field, i.e multiplication by scalar  is multiplication by where . So the previous means that the Tommy quaternions of the form commute and "associate" with everything.

But this means that the multiplication is bilinear: every element should it should have a representation.. e.g. multiplication by has a 4x4 matrix .
Obviously if it is not associative we "should not" have in general...

Probably my understanding of non-associative alg. is so poor that I'm missing something obvious.

MathStackExchange account:MphLee

Fundamental Law
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Messages In This Thread
" tommy quaternion " - by tommy1729 - 01/18/2021, 11:03 PM
RE: " tommy quaternion " - by marraco - 01/21/2021, 12:49 PM
RE: " tommy quaternion " - by tommy1729 - 01/21/2021, 01:17 PM
RE: " tommy quaternion " - by MphLee - 01/21/2021, 09:27 PM
RE: " tommy quaternion " - by tommy1729 - 01/21/2021, 11:47 PM
RE: " tommy quaternion " - by MphLee - 01/22/2021, 12:03 AM
RE: " tommy quaternion " - by tommy1729 - 01/22/2021, 12:15 AM
RE: " tommy quaternion " - by tommy1729 - 01/22/2021, 12:10 AM
RE: " tommy quaternion " - by MphLee - 01/22/2021, 12:41 AM
RE: " tommy quaternion " - by tommy1729 - 01/23/2021, 01:17 PM
RE: " tommy quaternion " - by marraco - 01/24/2021, 06:53 AM
RE: " tommy quaternion " - by tommy1729 - 02/12/2021, 11:17 PM
RE: " tommy quaternion " - by JmsNxn - 02/14/2021, 02:24 AM
RE: " tommy quaternion " - by tommy1729 - 03/23/2021, 01:21 PM
RE: " tommy quaternion " - by tommy1729 - 09/16/2021, 11:34 PM

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