اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAsymptotic Morphisms and Elliptic Operators over C*-algebras
82
0
0.0
(
0
)
تأليف
Jody Trout
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
This paper provides an E-theoretic proof of an exact form, due to E. Troitsky, of the Mischenko-Fomenko Index Theorem for elliptic pseudodifferential operators over a unital C*-algebra. The main ingredients in the proof are the use of asymptotic morphisms of Connes and Higson, vector bundle modification, a Baum-Douglas-type group, and a KK-argument of Kasparov.
قيم البحث
اقرأ أيضاً
We develop methods for computing graded K-theory of C*-algebras as defined in terms of Kasparov theory. We establish grad
Let $A$ be a graded C*-algebra. We characterize Kasparovs K-theory group $hat{K}_0(A)$ in terms of graded *-homomorphisms by proving a general converse to the functional calculus theorem for self-adjoint regular operators on graded Hilbert modules. A
n application to the index theory of elliptic differential operators on smooth closed manifolds and asymptotic morphisms is discussed.
We establish exact sequences in $KK$-theory for graded relative Cuntz-Pimsner algebras associated to nondegenerate $C^*$-correspondences. We use this to calculate the graded $K$-theory and $K$-homology of relative Cuntz-Krieger algebras of directed g
raphs for gradings induced by ${0,1}$-valued labellings of their edge sets.
Exploiting the graph product structure and results concerning amalgamated free products of C*-algebras we provide an explicit computation of the K-theoretic invariants of right-angled Hecke C*-algebras, including concrete algebraic representants of a
basis in K-theory. On the way, we show that these Hecke algebras are KK-equivalent with their undeformed counterparts and satisfy the UCT. Our results are applied to study the isomorphism problem for Hecke C*-algebras, highlighting the limits of K-theoretic classification, both for varying Coxeter type as well as for fixed Coxeter type.
We initiate the study of real $C^*$-algebras associated to higher-rank graphs $Lambda$, with a focus on their $K$-theory. Following Kasparov and Evans, we identify a spectral sequence which computes the $mathcal{CR}$ $K$-theory of $C^*_{mathbb R} (La
mbda, gamma)$ for any involution $gamma$ on $Lambda$, and show that the $E^2$ page of this spectral sequence can be straightforwardly computed from the combinatorial data of the $k$-graph $Lambda$ and the involution $gamma$. We provide a complete description of $K^{CR}(C^*_{mathbb R}(Lambda, gamma))$ for several examples of higher-rank graphs $Lambda$ with involution.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
