On formal theory of differential equations. III.

Jan Chrastina

Mathematica Bohemica (1991)

  • Volume: 116, Issue: 1, page 60-90
  • ISSN: 0862-7959

Abstract

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Elements of the general theory of Lie-Cartan pseudogroups (including the intransitive case) are developed within the framework of infinitely prolonged systems of partial differential equations (diffieties) which makes it independent of any particular realizations by transformations of geometric object. Three axiomatic approaches, the concepts of essential invariant, subgroup, normal subgroup and factorgroups are discussed. The existence of a very special canonical composition series based on Cauchy characteristics is proved and relations to the equivalence problem, theory of geometrical objects and connection theory are briefly mentioned.

How to cite

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Chrastina, Jan. "On formal theory of differential equations. III.." Mathematica Bohemica 116.1 (1991): 60-90. <http://eudml.org/doc/29350>.

@article{Chrastina1991,
abstract = {Elements of the general theory of Lie-Cartan pseudogroups (including the intransitive case) are developed within the framework of infinitely prolonged systems of partial differential equations (diffieties) which makes it independent of any particular realizations by transformations of geometric object. Three axiomatic approaches, the concepts of essential invariant, subgroup, normal subgroup and factorgroups are discussed. The existence of a very special canonical composition series based on Cauchy characteristics is proved and relations to the equivalence problem, theory of geometrical objects and connection theory are briefly mentioned.},
author = {Chrastina, Jan},
journal = {Mathematica Bohemica},
keywords = {Lie-Cartan pseudogroups; diffieties; equivalence problem; Cauchy characteristics; composition series; geometrical object; diffieties; Lie-Cartan pseudogroups; equivalence problem},
language = {eng},
number = {1},
pages = {60-90},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On formal theory of differential equations. III.},
url = {http://eudml.org/doc/29350},
volume = {116},
year = {1991},
}

TY - JOUR
AU - Chrastina, Jan
TI - On formal theory of differential equations. III.
JO - Mathematica Bohemica
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 116
IS - 1
SP - 60
EP - 90
AB - Elements of the general theory of Lie-Cartan pseudogroups (including the intransitive case) are developed within the framework of infinitely prolonged systems of partial differential equations (diffieties) which makes it independent of any particular realizations by transformations of geometric object. Three axiomatic approaches, the concepts of essential invariant, subgroup, normal subgroup and factorgroups are discussed. The existence of a very special canonical composition series based on Cauchy characteristics is proved and relations to the equivalence problem, theory of geometrical objects and connection theory are briefly mentioned.
LA - eng
KW - Lie-Cartan pseudogroups; diffieties; equivalence problem; Cauchy characteristics; composition series; geometrical object; diffieties; Lie-Cartan pseudogroups; equivalence problem
UR - http://eudml.org/doc/29350
ER -

References

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  1. E. Cartan, Oeuvres complètes II, 2. Paris 1953. (1953) MR0058523
  2. E. Cartan, Oeuvres complète II, 2. Paris 1953. (1953) 
  3. J. Chrastina, On formal theory of differential equations I, Časopis pěst. mat. 111 (1986), 353-383. (1986) Zbl0638.35008MR0871713
  4. J. Chrastina, On formal theory of differential equations II, Časopis pěst. mat. 114 (1989) 60-105. (1989) Zbl0703.34001MR0990119
  5. J. Chrastina, From elementary algebra to Bäcklund transformations, Czechoslovak Math. J. 40 (1990), 239-257. (1990) Zbl0726.58041MR1046292
  6. H. Goldschmidt D. Spencer, 10.1007/BF02392044, Acta Math. 136 (1976), 103-170. (1976) MR0445566DOI10.1007/BF02392044
  7. V. W. Guillemin S. Sternberg, An algebraic model of transitive differential geometry, Bull. Amer. Math. Soc. 70 (1946), 16-47. (1946) MR0170295
  8. V. W. Guillemin S. Sternberg, 10.4310/jdg/1214427885, J. Diff. Geom. 1 (1967), 127-131. (1967) MR0222800DOI10.4310/jdg/1214427885
  9. T. Higa, On the isomorphic reduction of an invariant associated with a Lie pseudogroup, Comm. Math. Univ. Sancti Pauli 34 (1985), 163-175. (1985) Zbl0602.58057MR0815786
  10. V. G. Kac, Simple irreducible graded Lie algebras of finite growth, (in Russian). Izvěstija Akad. Nauk 32 (1968), 1323-1367. (1968) Zbl0222.17007MR0259961
  11. S. Lie, Die Grundlagen für die Theorie der unendlichen kontinuierlichen Transformationsgruppen, Ges. Abh. 6, Leipzig 1927, 310-364. (1927) 
  12. P. Molino, 10.1007/BFb0091884, Lecture Notes in Mathematics 588 (1977). (1977) Zbl0357.53022DOI10.1007/BFb0091884
  13. A. Nijenhuis, Natural bundles and their general properties, Differential Geometry in Honour of K. Yano, Kino Kuniya, Toki 1972, 271-277. (1972) Zbl0246.53018MR0380862
  14. J. F. Pommaret, Systems of Partial Differential Equations and Lie Pseudogroups, Math. and Its Аppl. 14 (1978); Russian transl. 1983. (1978) Zbl0418.35028MR0731697
  15. A. A. Rodrigues, Ngo van Que, 10.5802/aif.551, Аnn. Inst. Fourier 25 (1975), 251-282. (1975) DOI10.5802/aif.551
  16. S. Sternberg, Lectures on Differential Geometry, Prentice Hall, New Јersey 1964. (1964) Zbl0129.13102MR0193578
  17. V. V. Žarinov, On the Bäcklund correspondences, (in Russian). Matematičeskij sbornik 136 (1988), 274-291. (1988) 

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