# Multitwisted real spectral triples

@article{Dabrowski2019MultitwistedRS, title={Multitwisted real spectral triples}, author={Ludwik Da̧browski and Andrzej Sitarz}, journal={arXiv: Quantum Algebra}, year={2019} }

We generalize the notion of spectral triple with reality structure to multitwisted real spectral triples, the class of which is closed under the tensor product composition. In particular, we introduce a multitwisted order one condition (characterizing the Dirac operators as an analogue of first-order differential operator). This provides a unified description of the known examples, which include conformally rescaled triples and (on the algebraic level) triples on quantum disc and on quantum…

## 2 Citations

### Gauge transformations of spectral triples with twisted real structures

- Mathematics
- 2020

We study the coupling of spectral triples with twisted real structures to gauge fields in the framework of noncommutative geometry and, adopting Morita equivalence via modules and bimodules as a…

### Twisted Spectral Triples without the First-Order Condition

- Mathematics
- 2021

We extend twisted inner fluctuations to twisted spectral triples that do not meet the twisted first order condition, following what has been done in [6] for the non twisted case. We find a similar…

## References

SHOWING 1-10 OF 23 REFERENCES

### Type III and spectral triples

- Mathematics
- 2006

We explain how a simple twisting of the notion of spectral triple allows to incorporate type III examples, such as those arising from the transverse geometry of codimension one foliations. Since the…

### Noncommutative Circle Bundles and New Dirac Operators

- Mathematics
- 2013

We study spectral triples over noncommutative principal U(1) bundles. Basing on the classical situation and the abstract algebraic approach, we propose an operatorial definition for a connection and…

### On Twisting Real Spectral Triples by Algebra Automorphisms

- Mathematics
- 2016

We systematically investigate ways to twist a real spectral triple via an algebra automorphism and in particular, we naturally define a twisted partner for any real graded spectral triple. Among…

### On twisted reality conditions

- MathematicsLetters in Mathematical Physics
- 2018

We study the twisted reality condition of Brzeziński et al. (Math Phys Anal Geom 19(3):11, 2016), for spectral triples, in particular with respect to the product and the commutant. Motivated by this,…

### On the spectral characterization of manifolds

- Mathematics
- 2008

We show that the first five of the axioms we had formulated on spectral triples suffice (in a slightly stronger form) to characterize the spectral triples associated to smooth compact manifolds. The…

### An Asymmetric Noncommutative Torus

- Mathematics
- 2015

We introduce a family of spectral triples that describe the curved noncommuta- tive two-torus. The relevant family of new Dirac operators is given by rescaling one of two terms in the flat Dirac…

### The Gauss-Bonnet Theorem for the noncommutative two torus

- Mathematics
- 2009

In this paper we shall show that the value at the origin, �(0), of the zeta function of the Laplacian on the non-commutative two torus, endowed with its canonical conformal structure, is independent…

### Noncommutative Manifolds, the Instanton Algebra¶and Isospectral Deformations

- Mathematics
- 2001

Abstract: We give new examples of noncommutative manifolds that are less standard than the NC-torus or Moyal deformations of ℝn. They arise naturally from basic considerations of noncommutative…

### Moyal Planes are Spectral Triples

- Mathematics
- 2004

Axioms for nonunital spectral triples, extending those introduced in the unital case by Connes, are proposed. As a guide, and for the sake of their importance in noncommutative quantum field theory,…

### The term a_4 in the heat kernel expansion of noncommutative tori

- Mathematics
- 2016

We consider the Laplacian associated with a general metric in the canonical conformal structure of the noncommutative two torus, and calculate a local expression for the term a_4 that appears in its…