Differentiating the State Evaluation Map from Matrices to Functions on Projective Space
Abstract
The pure state evaluation map from Mn(C) to C(CPn-1) is a completely positive map of C*-algebras intertwining the Un symmetries on the two algebras. We show that it extends to a cochain map from the universal calculus on Mn(C) to the holomorphic ∂¯ calculus on CPn-1. The method uses connections on Hilbert C*-bimodules.
- Publication:
-
Symmetry
- Pub Date:
- February 2023
- DOI:
- 10.3390/sym15020474
- arXiv:
- arXiv:2210.07033
- Bibcode:
- 2023Symm...15..474A
- Keywords:
-
- matrix algebra;
- projective space;
- state;
- calculus;
- bimodule;
- Mathematics - Operator Algebras;
- Mathematics - Quantum Algebra;
- 58B34;
- 46L30
- E-Print:
- Comments welcome