Non-Compact Hopf Maps and Fuzzy Ultra-Hyperboloids

Understand

Fuzzy hyperboloids naturally emerge in the geometries of D-branes, twistor theory, and higher spin theories.

• In this work, we perform a systematic study of higher dimensional fuzzy hyperboloids (ultra-hyperboloids) based on non-compact Hopf maps.
• Two types of non-compact Hopf maps; split-type and hybrid-type, are introduced from the cousins of division algebras.
• We construct arbitrary even-dimensional fuzzy ultra-hyperboloids by applying the Schwinger operator formalism and indefinite Clifford algebras.