On algebraic endomorphisms of the Einstein gyrogroup

Abstract

We describe the structure of all continuous algebraic endomorphisms of the open unit ball $\mathbf{B}$ of ${\mathbb{R}}^3$ equipped with the Einstein velocity addition. We show that any nonzero such transformation originates from an orthogonal linear transformation on ${\mathbb{R}}^3$.

References in corpus (1)

• Distances of qubit density matrices on Bloch sphere

Cited by in corpus (1)

• On endomorphisms of the Einstein gyrogroup in arbitrary dimension