The $p$-cones in dimension $n\ge 3$ are not homogeneous when $p\ne 2$

Abstract

Using the T-algebra machinery we show that, up to linear isomorphism, the only strictly convex homogeneous cones in ${\Re }^n$ with $n\ge 3$ 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 $p\ne 2$, $1<p<\infty$ and $n\ge 3$, thus answering a problem proposed by Gowda and Trott.

7 pages. Typo fixes. To appear in Linear Algebra and its Applications

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