On algebraic endomorphisms of the Einstein gyrogroup. (English) Zbl 1325.83002
Summary: 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 \(\mathbb{R}^{3}\).{
©2015 American Institute of Physics}
©2015 American Institute of Physics}
MSC:
| 83A05 | Special relativity |
Keywords:
algebraic endomorphism; Einstein gyrogroup; Einstein velocity addition; orthogonal linear transformationReferences:
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