Mathematics – Differential Geometry
Scientific paper
2011-08-22
Mathematics
Differential Geometry
This paper is an extended version of "Smooth Localization in Noncommutative Geometry", arxiv:1108.4294v1 [math.DG], 22 Aug 201
Scientific paper
A (smooth) dynamical system with transformation group $\mathbb{T}^n$ is a triple $(A,\mathbb{T}^n,\alpha)$, consisting of a unital locally convex algebra $A$, the $n$-torus $\mathbb{T}^n$ and a group homomorphism $\alpha:\mathbb{T}^n\rightarrow\Aut(A)$, which induces a (smooth) continuous action of $\mathbb{T}^n$ on $A$. In this paper we present a new, geometrically oriented approach to the noncommutative geometry of principal torus bundles based on such dynamical systems. Our approach is inspired by the classical setting: In fact, after recalling the definition of a trivial noncommutative principal torus bundle, we introduce a convenient (smooth) localization method for noncommutative algebras and say that a dynamical system $(A,\mathbb{T}^n,\alpha)$ is called a noncommutative principal $\mathbb{T}^n$-bundle, if localization leads to a trivial noncommutative principal $\mathbb{T}^n$-bundle. We prove that this approach extends the classical theory of principal torus bundles and present a bunch of (non-trivial) noncommutative examples.
No associations
LandOfFree
A Geometric Approach to Noncommutative Principal Torus Bundles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Geometric Approach to Noncommutative Principal Torus Bundles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Geometric Approach to Noncommutative Principal Torus Bundles will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-175962