Re-evaluating real quaternions

Subject: Re: Quaternions
From: Pertti Lounesto <lounesto@dopey.hut.fi>
Date: 1997/05/02
Message-Id: <w0ipvvabgdt.fsf@dopey.hut.fi>
Newsgroups: sci.physics.electromag,sci.physics.relativity

"Srdjan Budisin" <srdjan@EUnet.yu> writes:
-I would like to know if complex quaternions are the same as octanions?

No, octonions are not the same as complex quaternions.
Complex quaternions are isomorphic to Pauli spin matrices.

"Srdjan Budisin" <srdjan@EUnet.yu> writes:
-octanions form an algebra which is not a dividsion algebra.

No, octonions do form a division algebra.
Also all non-zero octonions do admit an inverse.

"Srdjan Budisin" <srdjan@EUnet.yu> writes:
-In this case [of complex quaternions] we would be living in
-a 6-dimensional space and a 2-dimensional time.

No, a space-time even would be represented by sqrt(-1)ct+ix+jy+kz.

"Srdjan Budisin" <srdjan@EUnet.yu> writes:
-Maybe, Maxwell equations can be formulated in therms of quatrnions?
-Maybe, Special Theory of Relativity can be formulated using Quaternions.
-How about Quantum Mechanics?

Pertti Lounesto writes:
> No, No, Yes, if you mean real quaternions.
> Yes, Yes, Yes, for complex quaternions (called also biquaternions).

I took a look at Doug Sweetser's nice web- site
http://world.std.com/~sweetser/quaternions/qindex/qindex. html
and have to re-evaluate my position:
Maxwell equations can be formulated by real quaternions alone
(but only in Lorentz gauge, and by a second order diff-equation).
Special theory of relativity, the Lorentz transformations, can
be formulated by real quaternions alone (but the Lorentz trans-
formation will depend also on the point to be transformed).
--
Pertti Lounesto http://www.math.hut.fi/~lounesto