Callias-type operators associated to spectral triples

نویسندگان

چکیده

Callias-type (or Dirac-Schrödinger) operators associated to abstract semifinite spectral triples are introduced and their indices computed in terms of an index pairing derived from the triple. The result is then interpreted as theorem for a non-commutative analogue flow. Both even odd considered, both commutative examples given.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Discrete spectral triples converging to dirac operators

We exhibit a series of discrete spectral triples converging to the canonical spectral triple of a finite dimensional manifold. Thus we bypass the non-go theorem of Gökeler and Schücker. Sort of counterexample. In [2] Connes gave the most general example of non commutative manifolds defined from finite spectral triples, and such discrete manifolds were classified independently by Krajewsky [5, 6...

متن کامل

Dense domains, symmetric operators and spectral triples

This article is about erroneous attempts to weaken the standard definition of unbounded Kasparov module (or spectral triple). This issue has been addressed previously, but here we present concrete counterexamples to claims in the literature that Fredholm modules can be obtained from these weaker variations of spectral triple. Our counterexamples are constructed using self-adjoint extensions of ...

متن کامل

Spectral triples of weighted groups

We study spectral triples on (weighted) groups and consider functors between the categories of weighted groups and spectral triples. We study the properties of weights and the corresponding functor for spectral triples coming from discrete weighted groups.

متن کامل

On Certain Spectral Features Inherent to Scalar Type Spectral Operators

Important spectral features, such as the emptiness of the residual spectrum, countability of the point spectrum, provided the space is separable, and a characterization of spectral gap at 0, known to hold for bounded scalar type spectral operators, are shown to naturally transfer to the unbounded case. Curiosity is the lust of the mind.

متن کامل

Equivariant Spectral Triples

We present the review of noncommutative symmetries applied to Connes’ formulation of spectral triples. We introduce the notion of equivariant spectral triples with Hopf algebras as isometries of noncommutative manifolds, relate it to other elements of theory (equivariant K-theory, homology, equivariant differential algebras) and provide several examples of spectral triples with their isometries...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Noncommutative Geometry

سال: 2023

ISSN: ['1661-6960', '1661-6952']

DOI: https://doi.org/10.4171/jncg/505