Hodge theory for complexes over C*-algebras with an application to A-ellipticity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10315800" target="_blank" >RIV/00216208:11320/15:10315800 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s10455-015-9449-1" target="_blank" >http://dx.doi.org/10.1007/s10455-015-9449-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10455-015-9449-1" target="_blank" >10.1007/s10455-015-9449-1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Hodge theory for complexes over C*-algebras with an application to A-ellipticity

Popis výsledku v původním jazyce

For a class of co-chain complexes in the category of pre-Hilbert -modules, we prove that their cohomology groups equipped with the canonical quotient topology are pre-Hilbert -modules, and derive the Hodge theory and, in particular, the Hodge decomposition for them. As an application, we show that -elliptic complexes of pseudodifferential operators acting on sections of finitely generated projective -Hilbert bundles over compact manifolds belong to this class if the images of the continuous extensions of their associated Laplace operators are closed. Moreover, we prove that the cohomology groups of these complexes share the structure of the fibers, in the sense that they are also finitely generated projective Hilbert A-modules.

Název v anglickém jazyce

Hodge theory for complexes over C*-algebras with an application to A-ellipticity

Popis výsledku anglicky

For a class of co-chain complexes in the category of pre-Hilbert -modules, we prove that their cohomology groups equipped with the canonical quotient topology are pre-Hilbert -modules, and derive the Hodge theory and, in particular, the Hodge decomposition for them. As an application, we show that -elliptic complexes of pseudodifferential operators acting on sections of finitely generated projective -Hilbert bundles over compact manifolds belong to this class if the images of the continuous extensions of their associated Laplace operators are closed. Moreover, we prove that the cohomology groups of these complexes share the structure of the fibers, in the sense that they are also finitely generated projective Hilbert A-modules.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Annals of Global Analysis and Geometry

ISSN

0232-704X

e-ISSN

—

Svazek periodika

47

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

14

Strana od-do

359-372

Kód UT WoS článku

000352292200003

EID výsledku v databázi Scopus

2-s2.0-84939966776