We describe the structure of all continuous algebraic endomorphisms of the open unit ball B of ℝ3 equipped with the Einstein velocity addition. We show that any nonzero such transformation originates from an orthogonal linear transformation on ℝ3.
REFERENCES
1.
T.
Abe
, “Gyrometric preserving maps on Einstein gyrogroups, Möbius gyrogroups and proper velocity gyrogroups
,” Nonlinear Funct. Anal. Appl.
19
, 1
–17
(2014
).2.
G.
Cassinelli
, E.
De Vito
, P. J.
Lahti
, and A.
Levrero
, in The Theory of Symmetry Actions in Quantum Mechanics
, Lecture Notes in Physics
Vol. 654
(Springer
, 2004
).3.
A.
Einstein
, Einsteins Miraculous Years: Five Papers that Changed the Face of Physics
(Princeton University
, Princeton, NJ
, 1998
).4.
S.
Kim
, “Distances of qubit density matrices on Bloch sphere
,” J. Math. Phys.
52
, 102303
(2011
).5.
L.
Molnár
, in Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces
, Lecture Notes in Mathematics
Vol. 1895
(Springer
, 2007
), p. 236
.6.
L.
Molnár
and P.
Szokol
, “Transformations on positive definite matrices preserving generalized distance measures
,” Linear Algebra Appl.
466
, 141
–159
(2015
).7.
L.
Molnár
and D.
Virosztek
, “Continuous Jordan triple endomorphisms of ℙ2
,” J. Math. Anal. Appl.
(submitted).8.
A. A.
Ungar
, Analytic Hyperbolic Geometry and Albert Einsteins Special Theory of Relativity
(World Scientific
, Singapore
, 2008
).© 2015 AIP Publishing LLC.
2015
AIP Publishing LLC
You do not currently have access to this content.