Commutators of flows and fields

Markus Mauhart; Peter W. Michor

Archivum Mathematicum (1992)

  • Volume: 028, Issue: 3-4, page 229-236
  • ISSN: 0044-8753

Abstract

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The well known formula [ X , Y ] = 1 2 2 t 2 | 0 ( - t Y ø - t X ø t Y ø t X ) for vector fields X , Y is generalized to arbitrary bracket expressions and arbitrary curves of local diffeomorphisms.

How to cite

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Mauhart, Markus, and Michor, Peter W.. "Commutators of flows and fields." Archivum Mathematicum 028.3-4 (1992): 229-236. <http://eudml.org/doc/247328>.

@article{Mauhart1992,
abstract = {The well known formula $[X,Y]=\tfrac\{1\}\{2\}\tfrac\{\partial ^2\}\{\partial t^2\}|_0 (^Y_\{-t\}ø^X_\{-t\}ø^Y_tø^X_t)$ for vector fields $X$, $Y$ is generalized to arbitrary bracket expressions and arbitrary curves of local diffeomorphisms.},
author = {Mauhart, Markus, Michor, Peter W.},
journal = {Archivum Mathematicum},
keywords = {commutators; flows; vector fields; commutators; flows; Lie bracket; vector fields; Trotter product formula},
language = {eng},
number = {3-4},
pages = {229-236},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Commutators of flows and fields},
url = {http://eudml.org/doc/247328},
volume = {028},
year = {1992},
}

TY - JOUR
AU - Mauhart, Markus
AU - Michor, Peter W.
TI - Commutators of flows and fields
JO - Archivum Mathematicum
PY - 1992
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 028
IS - 3-4
SP - 229
EP - 236
AB - The well known formula $[X,Y]=\tfrac{1}{2}\tfrac{\partial ^2}{\partial t^2}|_0 (^Y_{-t}ø^X_{-t}ø^Y_tø^X_t)$ for vector fields $X$, $Y$ is generalized to arbitrary bracket expressions and arbitrary curves of local diffeomorphisms.
LA - eng
KW - commutators; flows; vector fields; commutators; flows; Lie bracket; vector fields; Trotter product formula
UR - http://eudml.org/doc/247328
ER -

References

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  1. Linear spaces and differentiation theory, Pure and Applied Mathematics, J. Wiley, Chichester, 1988. (1988) MR0961256
  2. Natural operators in differential geometry, to appear, Springer-Verlag. MR1202431
  3. A convenient setting for real analytic mappings, Acta Mathematica 165 (1990), 105–159. (1990) MR1064579
  4. Aspects of the theory of infinite dimensional manifolds, Differential Geometry and Applications 1(1) (1991). (1991) MR1244442
  5. Foundations of Global Analysis, A book in the early stages of preparation. 
  6. A convenient setting for holomorphy, Cahiers Top. Géo. Diff. 26 (1985), 273–309. (1985) MR0796352
  7. Iterierte Lie Ableitungen und Integrabilität, Diplomarbeit, Universität Wien, 1990. (1990) 
  8. Natural vector bundles and natural differential operators, American J. of Math. 100 (1978), 775–828. (1978) MR0509074

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