Complex Lipschitz structures and bundles of complex Clifford modules

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Title
Complex Lipschitz structures and bundles of complex Clifford modules
Author(s)
Lazaroiu C.I.; Shahbazi C.S.
Publication Date
2018-12
Journal
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v.61, no., pp.147 - 169
Publisher
ELSEVIER SCIENCE BV
Abstract
Let (M,g) be a pseudo-Riemannian manifold of signature (p,q). We construct mutually quasi-inverse equivalences between the groupoid of bundles of weakly-faithful complex Clifford modules on (M,g) and the groupoid of reduced complex Lipschitz structures on (M,g). As an application, we show that (M,g) admits a bundle of irreducible complex Clifford modules if and only if it admits either a Spinc(p,q) structure (when p+q is odd) or a Pinc(p,q) structure (when p+q is even). When p−q≡83,4,6,7, we compare with the classification of bundles of irreducible real Clifford modules which we obtained in previous work. The results obtained in this note form a counterpart of the classification of bundles of faithful complex Clifford modules which was previously given by T. Friedrich and A. Trautman. © 2018 Elsevier B.V
URI
https://pr.ibs.re.kr/handle/8788114/5039
ISSN
0926-2245
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > Journal Papers (저널논문)
Files in This Item:
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