Kenkyu-Honkan bldg. 1F - Kobayashi Hall
Diffeomorphism for fuzzy spaces
- Dr. Takashi MATSUMOTO
Fuzzy spaces are known as a typical example of noncommutative geometry and expected to describe the fundamental structure of space-time. However, the mechanism to describe gravity in the framework of fuzzy spaces remains to be completely elucidated. In order to understand the mechanism, we focus on the notion of diffeomorphisms, which plays a key role in the classical theory of gravity. In this talk, we propose a formulation of the diffeomorphisms for fuzzy spaces in terms of the Berezin-Toeplitz quantization map, which is introduced in the context of geometric quantization. We apply this formulation to 2-sphere as an example and obtain new matrix configurations that are diffeomorphic to the standard fuzzy sphere given by the generators of SU(2) Lie algebra.