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arXiv · 1701.05801

The $p$-cones in dimension $n \geq 3$ are not homogeneous when $p\neq 2$

Masaru Ito·Bruno F. Lourenço
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Abstract

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

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Masaru Ito, Bruno F. Lourenço. 2017-08-01. The $p$-cones in dimension $n \geq 3$ are not homogeneous when $p\neq 2$. https://doi.org/10.1016/j.laa.2017.07.029

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