The p-cones in dimension n ≥ 3 are not homogeneous when p ≠ 2

Using the T-algebra machinery we show that, up to linear isomorphism, the only strictly convex homogeneous cones in Rn (n≥3) are the 2-cones, also known as Lorentz cones or second order cones. In particular, this shows that the p-cones are not homogeneous when p≠2, 1