Natural Science Forum / Physics / Research / May 2008

On 25 mayo, 01:53, "ariv...@unizar.es" <Al.Riv...@gmail.com> wrote:

The longer posting.

I am interested on this question, of course, to study the breaking
from (SU(3))x(SU(2)xU(1)) to SU(3)xU(1). My related interest is to
leart about [principal homogeneous] spaces where the (q-?)group acts
regularly, and to see if these spaces are commutative or not, and to
learn which is the minimum dimension of these spaces.

The idea is that SU(3)xSU(2)xU(1) needs to act in an space of
dimension 7 as minimum, while SU(3)xU(1) needs only and space of
dimension 5.  So the broken spaces of our beloved Standard Model
should live somewhere in the middle.

The hope is that the breaking of symmetry in the standard model could
be related to the need of fitting it in a Kaluza Klein compact space
of only six extra dimensions.

It could be also possible to consider G/K with K some kind of deformed
subgroup of G. In general if we have K \in H \in G and we have
quotients G/H and H/K such that the groups G and H have regular
actions there respectively, it seems intuitive that under some general
condition the dimension of (G/H) should be greater than the dimension
of (H/K)... but intuitive does not translate to true, and I have not
clue in any case about how the situation generalizes to the deformed
case.

Alejandro

(PS a general course on group actions, if Helgason is not available
online:
https://www8.imperial.ac.uk/content/dav/ad/workspaces/mathematics/students/ug/co
urse_material/lie_groups2.PDF.)