Re: Rotations in 4D
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Lanco
Mar 19, 2013, 7:39:46 PM3/19/13
to Geometric_Algebra
As you mention, the quaternions H can be identified as Clifford
algebra with the even part of the geometric algebra R(3,0). By using
R^4 the H-algebra structure is not inherited.
In the following a,b are in H and with squared norm 1.
The sandwich formula x->a x/a gives all rotations of R(3,0).
This gives all isometries of H with 1 fixed.
By norm calculations x->a x and x->x b are isometries of H, etc.
You may look at p. 62-65 in Porteous, Clifford algebras and the
classical groups.
lanco
algebra with the even part of the geometric algebra R(3,0). By using
R^4 the H-algebra structure is not inherited.
In the following a,b are in H and with squared norm 1.
The sandwich formula x->a x/a gives all rotations of R(3,0).
This gives all isometries of H with 1 fixed.
By norm calculations x->a x and x->x b are isometries of H, etc.
You may look at p. 62-65 in Porteous, Clifford algebras and the
classical groups.
lanco
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