The
-algebra
of continuous functions on the quantum quaternion sphere
can be identified with the
quotient algebra
. In the
commutative case, i.e., for
,
the topological space
is homeomorphic to the odd-dimensional sphere
. In
this paper, we prove the noncommutative analogue of this result. Using homogeneous
-extension theory, we
prove that the
-algebra
is isomorphic
to the
-algebra
. This further implies that
for different values of
in
, the
-algebras underlying the
noncommutative spaces
are isomorphic.
