A Farewell To Unimodularity

TL;DR

This paper reinterprets the unimodularity condition in almost commutative geometries as central extensions of spin lifts, enabling the computation of fermion hypercharges within Connes' standard model framework.

Contribution

It introduces a novel interpretation of unimodularity as central extensions, facilitating hypercharge calculations in noncommutative geometry models.

Findings

Hypercharges of fermions can be computed using the new interpretation.

Provides a geometric understanding of the unimodularity condition.

Links algebraic structures to physical charge assignments.

Abstract

We interpret the unimodularity condition in almost commutative geometries as central extensions of spin lifts. In Connes' formulation of the standard model this interpretation allows to compute the hypercharges of the fermions.