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Motivated by optimization considerations, we consider cones in Rn – to be called special Bishop–Phelps cones – of the form {(t,x):t≥||x||}, where ||⋅|| is a norm on Rn−1. We show that when n≥3, such cones are always irreducible. Defining the Lyapunov rank of a proper cone K as the dimension of the Lie algebra of the automorphism group of K, we show that the Lyapunov rank of any special Bishop–Phelps...
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