Last Updated：2022/12/24
The other class 𝒞₂ of loops consists of 3-dimensional connected differentiable left A-loops such that the group G=PSL_2( ℝ) ltimes ℝ³ is the group topologically generated by the left translations The loops in this class can be represented by two real parameters a,b and form precisely two isomorphism classes, which coincide with the isotopism classes.
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The
other
class
𝒞₂
of
loops
consists
of
3-dimensional
connected
differentiable
left
A-loops
such
that
the
group
G=PSL_2(
ℝ)
ltimes
ℝ³
is
the
group
topologically
generated
by
the
left
translations
The
loops
in
this
class
can
be
represented
by
two
real
parameters
a,b
and
form
precisely
two
isomorphism
classes,
which
coincide
with
the
isotopism
classes.
