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- W4288284210 abstract "We study the Poincar'e disk $d={zina: |z|<1}$ of a C$^*$-algebra $a$ as a homogeneous space under the action of an appropriate Banach-Lie group $u(theta)$ of $2times 2$ matrices with entries in $a$. We define on $d$ a homogeneous Kahler structure in a non commutative sense. In particular, this Kahler structure defines on $d$ a homogeneous symplectic structure under the action of $u(theta)$. This action has a moment map that we explicitly compute. In the presence of a trace in $a$, we show that the moment map has a convex image when restricted to appropriate subgroups of $u(theta)$, resembling the classical result of Atiyah-Guillmien-Sternberg." @default.
- W4288284210 created "2022-07-28" @default.
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- W4288284210 date "2019-07-10" @default.
- W4288284210 modified "2023-09-27" @default.
- W4288284210 title "A non commutative Kahler structure on the Poincar'e disk of a C*-algebra" @default.
- W4288284210 doi "https://doi.org/10.48550/arxiv.1907.04912" @default.
- W4288284210 hasPublicationYear "2019" @default.
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