The integrability of a field of endomorphisms

Gerard Thompson

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 4, page 605-611
  • ISSN: 0862-7959

Abstract

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A Theorem is proved that gives intrinsic necessary and sufficient conditions for the integrability of a zero-deformable field of endomorphisms. The Theorem is proved by reducing to a special case in which the endomorphism field is nilpotent. Many arguments used in the derivation of similar results are simplified, principally by means of using quotient rather than subspace constructions.

How to cite

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Thompson, Gerard. "The integrability of a field of endomorphisms." Mathematica Bohemica 127.4 (2002): 605-611. <http://eudml.org/doc/249030>.

@article{Thompson2002,
abstract = {A Theorem is proved that gives intrinsic necessary and sufficient conditions for the integrability of a zero-deformable field of endomorphisms. The Theorem is proved by reducing to a special case in which the endomorphism field is nilpotent. Many arguments used in the derivation of similar results are simplified, principally by means of using quotient rather than subspace constructions.},
author = {Thompson, Gerard},
journal = {Mathematica Bohemica},
keywords = {integrability; endomorphism; quotient space; integrability; endomorphism; quotient space},
language = {eng},
number = {4},
pages = {605-611},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The integrability of a field of endomorphisms},
url = {http://eudml.org/doc/249030},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Thompson, Gerard
TI - The integrability of a field of endomorphisms
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 4
SP - 605
EP - 611
AB - A Theorem is proved that gives intrinsic necessary and sufficient conditions for the integrability of a zero-deformable field of endomorphisms. The Theorem is proved by reducing to a special case in which the endomorphism field is nilpotent. Many arguments used in the derivation of similar results are simplified, principally by means of using quotient rather than subspace constructions.
LA - eng
KW - integrability; endomorphism; quotient space; integrability; endomorphism; quotient space
UR - http://eudml.org/doc/249030
ER -

References

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  1. A remark on the Nijenhius tensor, Pacific J. Math. 12 (1961), 963–977. (1961) 
  2. 10.1017/S0305004100070262, Math. Proc. Camb. Phil. Soc. 110 (1991), 207–224. (1991) MR1104616DOI10.1017/S0305004100070262
  3. 10.5802/aif.246, Ann. Inst. Fourier 16 (1966), 329–387. (1966) MR0212720DOI10.5802/aif.246
  4. Intégrabilité d’un tenseur de type (1,1) et structure symplectique du fibré cotangent, C.R. Acad. Sci., Paris, Sér. I 301 (1985), 923–925. (1985) Zbl0592.53024MR0829063
  5. Classification locale d’un couple de formes symplectiques Poisson-compatible, C.R. Acad. Sci., Paris, t. 308, Série I (1989), 575–578. (1989) MR1001810

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