The Jordan algebraic structure of the rotated quadratic cone

In this paper, we look into the rotated quadratic cone and analyze its algebraic structure. We construct an algebra associated with this cone and show that this algebra is a Euclidean Jordan algebra (EJA) with a certain inner product. We also demonstrate some spectral and algebraic characteristics of this EJA. The rotated quadratic cone is then proven to be the cone of squares of the generated EJA. The obtained results can help optimization researchers improve specialized interior-point algorithms for rotated quadratic cone programming based on the generated EJA. Additionally, since it is known that the rotated quadratic cone is a special case of the power cone, another reason for this study may be to open the door to understanding the algebraic structure of the general power cone in the future.