
TL;DR
This paper proves that the special unitary group SU_3 over the real numbers is a Cayley group, extending previous results on the Cayley property of SL_3 over algebraically closed fields, and discusses the Cayley property of SL_{3,R}.
Contribution
It establishes that SU_3 over R is a Cayley group, expanding the class of known Cayley groups and extending prior work on SL_3.
Findings
SU_3 is a Cayley group over R
Extension of Popov's 1975 result on SL_3
Discussion on whether SL_{3,R} is Cayley
Abstract
A linear algebraic group G is over a field K is called a Cayley group if it admits a Cayley map, i.e., a G-equivariant K-birational isomorphism between the group variety G and its Lie algebra. We prove that the special unitary group in 3 variables SU_3 is a Cayley group over R, thus extending a result of V.L. Popov, who proved in 1975 that the special linear group in 3 variables SL_3 over an algebraically closed field of characteristic 0 is Cayley. We also discuss the question whether the R-group SL_{3,R} is Cayley.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Advanced Topics in Algebra
