ترغب بنشر مسار تعليمي؟ اضغط هنا

The non-unital version of Connes theorem on the Hochschild class of the Chern character

204   0   0.0 ( 0 )
 نشر من قبل Adam Rennie
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We offer a short proof of Connes Hochschild class of the Chern character formula for non-unital semifinite spectral triples. The proof is simple due to its reliance on the authors extensive work on a refined version of the local index formula, and the consequent understanding of the passage from generalised residues of zeta functions to representations in terms of singular traces.



قيم البحث

اقرأ أيضاً

103 - A. Carey , A. Rennie , F. Sukochev 2014
We study notions of measurability for singular traces, and characterise universal measurability for operators in Dixmier ideals. This measurability result is then applied to improve on the various proofs of Connes identification of the Hochschild cla ss of the Chern character of Dixmier summable spectral triples. The measurability results show that the identification of the Hochschild class is independent of the choice of singular trace. As a corollary we obtain strong information on the asymptotics of the eigenvalues of operators naturally associated to spectral triples (A,H,D) and Hochschild cycles for A.
We compute the Chern-Connes character (a map from the $K$-theory of a C$^*$-algebra under the action of a Lie group to the cohomology of its Lie algebra) for the $L^2$-norm closure of the algebra of all classical zero-order pseudodifferential operato rs on the sphere under the canonical action of ${rm SO}(3)$. We show that its image is $mathbb{R}$ if the trace is the integral of the principal symbol.
We construct a Chern character map from the K-theory of the reduced C^* algebra of the p-adic GL(n) with values in the periodic cyclic homology of the Schwartz algebra of this group. We prove that this map is an isomorphism after tensoring with C by comparing an explicit formula, stated in the algebraic case by Cuntz and Quillen, with the classical Chern character. This Chern character is a crucial ingredient in the proof of the Baum-Connes conjecture for the p-adic GL(n) due to Baum, Higson and Plymen.
157 - Efton Park 2010
Let $X$ be a compact Hausdorff space, let $Gamma$ be a discrete group that acts continuously on $X$ from the right, define $widetilde{X} = {(x,gamma) in X times Gamma : xcdotgamma= x}$, and let $Gamma$ act on $widetilde{X}$ via the formula $(x,gamma) cdotalpha = (xcdotalpha, alpha^{-1}gammaalpha)$. Results of P. Baum and A. Connes, along with facts about the Chern character, imply that $K^i_Gamma(X) otimes mathbb{C} cong K^i(widetilde{X}slashGamma) otimes mathbb{C}$ for $i = 0, -1$. In this note, we present an example where the groups $K^i_Gamma(X)$ and $K^i(widetilde{X}slashGamma)$ are not isomorphic.
We introduce the notion of a {vartheta}-summable Fredholm module over a locally convex dg algebra {Omega} and construct its Chern character as a cocycle on the entire cyclic complex of {Omega}, extending the construction of Jaffe, Lesniewski and Oste rwalder to a differential graded setting. Using this Chern character, we prove an index theorem involving an abstract version of a Bismut-Chern character constructed by Getzler, Jones and Petrack in the context of loop spaces. Our theory leads to a rigorous construction of the path integral for N=1/2 supersymmetry which satisfies a Duistermaat-Heckman type localization formula on loop space.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا