Twisted geometry for submanifolds of ${\mathbb{R}}^n$

Abstract

This is a friendly introduction to our recent general procedure for constructing noncommutative deformations of an embedded submanifold $M$ of ${\mathbb{R}}^n$ determined by a set of smooth equations $f^a(x)=0$. We use the framework of Drinfel'd twist deformation of differential geometry pioneered in [Aschieri et al., Class. Quantum Gravity 23 (2006), 1883]; the commutative pointwise product is replaced by a (generally noncommutative) $\star$-product induced by a Drinfel'd twist.

20 pages. Submitted to PoS, as a contribution to the Proceedings of Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity", more precisely to the "Workshop on Quantum Geometry, Field Theory and Gravity", 20-27 September 2021

References in corpus (3)

• Noncommutative Gravity Solutions
• Braided Cartan Calculi and Submanifold Algebras
• Cartan structure equations and Levi-Civita connection in noncommutative geometry