Journal of Lie Theory

no. 1
On Penney's Cayley Transform of a Homogeneous Siegel Domain
Journal of Lie Theory, Volume 11 (2001) no. 1, pp. 185-206
We introduce a Cayley transform C of a homogeneous Siegel domain D as a slight modification of Penney's one. We give an explicit formula to the inverse map of C, and thus clarify the biholomorphic nature of C in a direct and visible manner. When D is quasisymmetric, our Cayley transform C is shown to be naturally coincident with Dorfmeister's one. A phenomenon which does not appear in the case of quasisymmetric domains is presented by an example in the last section.
DOI: 10.5802/jolt.229
Classification: 32M15
Keywords: Cayley transform, Siegel domain, quasisymmetric domain, \(j\)-algebra 
@article{JOLT_2001_11_1_a10,
     author = {T. Nomura},
     title = {On {Penney's} {Cayley} {Transform} of a {Homogeneous} {Siegel} {Domain}},
     journal = {Journal of Lie Theory},
     pages = {185--206},
     year = {2001},
     volume = {11},
     number = {1},
     doi = {10.5802/jolt.229},
     zbl = {0977.32015},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.229/}
}
TY  - JOUR
AU  - T. Nomura
TI  - On Penney's Cayley Transform of a Homogeneous Siegel Domain
JO  - Journal of Lie Theory
PY  - 2001
SP  - 185
EP  - 206
VL  - 11
IS  - 1
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.229/
DO  - 10.5802/jolt.229
ID  - JOLT_2001_11_1_a10
ER  - 
%0 Journal Article
%A T. Nomura
%T On Penney's Cayley Transform of a Homogeneous Siegel Domain
%J Journal of Lie Theory
%D 2001
%P 185-206
%V 11
%N 1
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.229/
%R 10.5802/jolt.229
%F JOLT_2001_11_1_a10
T. Nomura. On Penney's Cayley Transform of a Homogeneous Siegel Domain. Journal of Lie Theory, Volume 11 (2001) no. 1, pp. 185-206. doi: 10.5802/jolt.229

Cited by Sources: