Spin groups of super metrics and a theorem of Rogers

JOURNAL OF GEOMETRY AND PHYSICS

卷:111

Article

Fulp, Ronald¹ 

[1] North Carolina State Univ, Dept Math, Box 8205, Raleigh, NC 27695 USA

关键词: G(infinity)-supermanifolds;    Super Riemannian metrics;    Canonical forms;    Local isometry groups;    Super Lie groups;    Conventional super Lie algebras;   

DOI  :  10.1016/j.geomphys.2016.10.009

来源: Elsevier

【 摘 要 】

We derive the canonical forms of super Riemannian metrics and the local isometry groups of such metrics. For certain super metrics we also compute the simply connected covering groups of the local isometry groups and interpret these as local spin groups of the super metric. Super metrics define reductions OSg of the relevant frame bundle. When principal bundles (S) over bar (g) exist with structure group the simply connected covering group (G) over bar of the structure group of OSg, representations of (G) over bar define vector bundles associated to (S) over bar (g) whose sections are spinor fields associated with the super metric g. Using a generalization of a Theorem of Rogers, which is itself one of the main results of this paper, we show that for super metrics we call body reducible, each such simply connected covering group 0 is a super Lie group with a conventional super Lie algebra as its corresponding super Lie algebra. Some of our results were known to DeWitt (1984) using formal Grassmann series and others were known by Rogers using finitely many Grassmann generators and passing to a direct limit. We work exclusively in the category of G(infinity) supermanifolds with G(infinity) mappings. Our supernumbers are infinite series of products of Grassmann generators subject to convergence in the l(1) norm introduced by Rogers (1980, 2007). (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free