The Chern–Galois character

Tomasz Brzeziński; Piotr M. Hajac

doi:10.1016/j.crma.2003.11.009

Algebra/Topology

The Chern–Galois character

Presented by: Alain Connes

Tomasz Brzeziński ¹; Piotr M. Hajac ^2,³

¹ Department of Mathematics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, UK
² Instytut Matematyczny, Polska Akademia Nauk, ul. Śniadeckich 8, Warszawa, 00-956 Poland
³ Katedra Metod Matematycznych Fizyki, Uniwersytet Warszawski ul. Hoża 74, Warszawa, 00-682 Poland

Comptes Rendus. Mathématique, Volume 338 (2004) no. 2, pp. 113-116.

Abstract
Résumé

Following the idea of Galois-type extensions and entwining structures, we define the notion of a principal extension of noncommutative algebras. We show that modules associated to such extensions via finite-dimensional corepresentations are finitely generated projective, and determine an explicit formula for the Chern character applied to the modules so obtained.

Nous nous inspirons des extensions de type Galois et des structures enlacées pour définir la notion d'extension principale d'algèbres non commutatives. Nous montrons que les modules associés à de telles extensions au travers de coreprésentations de dimension finie sont projectifs et de type fini, et nous déterminons une formule explicite pour le caractère de Chern appliqué aux modules ainsi obtenus.

Received: 2003-07-31
Accepted: 2003-11-12
Published online: 2003-12-30

DOI: 10.1016/j.crma.2003.11.009

Author's affiliations:

Tomasz Brzeziński ¹; Piotr M. Hajac ^{2, 3}

¹ Department of Mathematics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, UK
² Instytut Matematyczny, Polska Akademia Nauk, ul. Śniadeckich 8, Warszawa, 00-956 Poland
³ Katedra Metod Matematycznych Fizyki, Uniwersytet Warszawski ul. Hoża 74, Warszawa, 00-682 Poland

@article{CRMATH_2004__338_2_113_0,
     author = {Tomasz Brzezi\'nski and Piotr M. Hajac},
     title = {The {Chern{\textendash}Galois} character},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {113--116},
     publisher = {Elsevier},
     volume = {338},
     number = {2},
     year = {2004},
     doi = {10.1016/j.crma.2003.11.009},
     language = {en},
}

TY  - JOUR
AU  - Tomasz Brzeziński
AU  - Piotr M. Hajac
TI  - The Chern–Galois character
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 113
EP  - 116
VL  - 338
IS  - 2
PB  - Elsevier
DO  - 10.1016/j.crma.2003.11.009
LA  - en
ID  - CRMATH_2004__338_2_113_0
ER  -

%0 Journal Article
%A Tomasz Brzeziński
%A Piotr M. Hajac
%T The Chern–Galois character
%J Comptes Rendus. Mathématique
%D 2004
%P 113-116
%V 338
%N 2
%I Elsevier
%R 10.1016/j.crma.2003.11.009
%G en
%F CRMATH_2004__338_2_113_0

Tomasz Brzeziński; Piotr M. Hajac. The Chern–Galois character. Comptes Rendus. Mathématique, Volume 338 (2004) no. 2, pp. 113-116. doi : 10.1016/j.crma.2003.11.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.11.009/

References
Cited by

[1] F. Bonechi, L. Da̧browski, N. Ciccoli, M. Tarlini, Bijectivity of the canonical map for the noncommutative instanton bundle, J. Geom. Phys., in press

[2] T. Brzeziński On modules associated to coalgebra Galois extensions, J. Algebra, Volume 215 (1999), pp. 290-317

[3] T. Brzeziński; P.M. Hajac Coalgebra extensions and algebra coextensions of Galois type, Comm. Algebra, Volume 27 (1999), pp. 1347-1367

[4] T. Brzeziński; S. Majid Coalgebra bundles, Comm. Math. Phys., Volume 191 (1998), pp. 467-492

[5] H. Cartan; S. Eilenberg Homological Algebra, Princeton University Press, Princeton, NJ, 1956

[6] A. Connes Non-commutative differential geometry, Inst. Hautes Études Sci. Publ. Math., Volume 62 (1985), pp. 257-360

[7] J. Cuntz; D. Quillen Algebra extensions and nonsingularity, J. Amer. Math. Soc., Volume 8 (1995), pp. 251-289

[8] L. Da̧browski; H. Grosse; P.M. Hajac Strong connections and Chern–Connes pairing in the Hopf–Galois theory, Comm. Math. Phys., Volume 220 (2001), pp. 301-331

[9] P.M. Hajac; R. Matthes; W. Szymański Chern numbers for two families of noncommutative Hopf fibrations, C. R. Acad. Sci. Paris, Ser. I, Volume 336 (2003), pp. 925-930

[10] J.-L. Loday Cyclic Homology, Springer-Verlag, Berlin, 1998

[11] E.F. Müller; H.-J. Schneider Quantum homogeneous spaces with faithfully flat module structures, Israel J. Math., Volume 111 (1999), pp. 157-190

[12] P. Schauenburg, H.-J. Schneider, Galois-type extensions and Hopf algebras, in preparation

[13] H.-J. Schneider Principal homogeneous spaces for arbitrary Hopf algebras, Israel J. Math., Volume 72 (1990), pp. 167-195

Cited by Sources:

Comments - Policy