Abstract
A binary operation ⊕ is defined in any bounded symmetric domain D turning it into a groupoid with relaxed associative and commutative laws, called a gyrogroup. It is shown that the group Aut(D) of all holomorphic automorphisms of D has a gyrosemidirect product structure, a structure that generalizes the semidirect product one. More specifically, the group Aut(D) turns out to be the gyrosemidirect product of the (nongroup) gyrogroup (D, ⊕) and the isotropic group K of D.
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Friedman, Y., Ungar, A.A. Gyrosemidirect Product Structure of Bounded Symmetric Domains. Results. Math. 26, 28–38 (1994). https://doi.org/10.1007/BF03322286
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DOI: https://doi.org/10.1007/BF03322286