General Jacobi identity revisited
type: Item
instance of: scholarly article
title: General Jacobi identity revisited
zbMATH Open document ID: 0942.58006
DOI: 10.1023/A:1026670206427
author: Hirokazu Nishimura
published in: International Journal of Theoretical Physics
publication date: 1999-11-18T00:00:00Z
review text: This paper explores the Jacobi identity in the context of synthetic differential geometry (SDG). It uses the theory of microsquares originally developed by \textit{A. Kock} and \textit{R. Lavendhomme} [Cah. Topologie Géom. Différ. 25, 311-324 (1984; Zbl 0564.18009)] to study the Lie bracket for vector fields in SDG. Their work was developed further by the author [Int. J. Theor. Phys. 36, No. 5, 1099-1131 (1997; Zbl 0884.18014)], where he proved a generalized Jacobi identity. The paper under review seeks to redo the proof in a more intuitive and clearer fashion. It is essentially a diagram chasing argument once set up properly with some rather elaborate calculations, as might be expected.
Mathematics Subject Classification ID: 58A03
Mathematics Subject Classification ID: 18F15
Mathematics Subject Classification ID: 51K10
zbMATH DE Number: 1364417
zbMATH Keywords: Jacobi identity
zbMATH Keywords: synthetic differential geometry
zbMATH Keywords: microsquares
reviewed by: K. I. Rosenthal
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1364417