| Title:
|
On formal theory of differential equations. III. (English) |
| Author:
|
Chrastina, Jan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
116 |
| Issue:
|
1 |
| Year:
|
1991 |
| Pages:
|
60-90 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Lie-Cartan pseudogroups |
| Keyword:
|
diffieties |
| Keyword:
|
equivalence problem |
| Keyword:
|
Cauchy characteristics |
| Keyword:
|
composition series |
| Keyword:
|
geometrical object |
| MSC:
|
22E65 |
| MSC:
|
35A30 |
| MSC:
|
58A17 |
| MSC:
|
58H05 |
| idZBL:
|
Zbl 0728.58041 |
| idMR:
|
MR1100425 |
| DOI:
|
10.21136/MB.1991.126196 |
| . |
| Date available:
|
2009-09-24T20:43:07Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126196 |
| . |
| Reference:
|
[1] E. Cartan: Oeuvres complètes II.2. Paris 1953. MR 0058523 |
| Reference:
|
[2] E. Cartan: Oeuvres complète II.2. Paris 1953. |
| Reference:
|
[3] J. Chrastina: On formal theory of differential equations I.Časopis pěst. mat. 111 (1986), 353-383. Zbl 0638.35008, MR 0871713 |
| Reference:
|
[4] J. Chrastina: On formal theory of differential equations II.Časopis pěst. mat. 114 (1989) 60-105. Zbl 0703.34001, MR 0990119 |
| Reference:
|
[5] J. Chrastina: From elementary algebra to Bäcklund transformations.Czechoslovak Math. J. 40 (1990), 239-257. Zbl 0726.58041, MR 1046292 |
| Reference:
|
[6] H. Goldschmidt D. Spencer: On non-linear cohomology of Lie equations I.Acta Math. 136 (1976), 103-170. MR 0445566, 10.1007/BF02392044 |
| Reference:
|
[7] V. W. Guillemin S. Sternberg: An algebraic model of transitive differential geometry.Bull. Amer. Math. Soc. 70 (1946), 16-47. MR 0170295 |
| Reference:
|
[8] V. W. Guillemin S. Sternberg: The Lewy counterexample and the local equivalence problem for G-structures.J. Diff. Geom. 1 (1967), 127-131. MR 0222800, 10.4310/jdg/1214427885 |
| Reference:
|
[9] T. Higa: On the isomorphic reduction of an invariant associated with a Lie pseudogroup.Comm. Math. Univ. Sancti Pauli 34 (1985), 163-175. Zbl 0602.58057, MR 0815786 |
| Reference:
|
[10] V. G. Kac: Simple irreducible graded Lie algebras of finite growth.(in Russian). Izvěstija Akad. Nauk 32 (1968), 1323-1367. Zbl 0222.17007, MR 0259961 |
| Reference:
|
[11] S. Lie: Die Grundlagen für die Theorie der unendlichen kontinuierlichen Transformationsgruppen.Ges. Abh. 6, Leipzig 1927, 310-364. |
| Reference:
|
[12] P. Molino: Théorie des G-structures, le problème d'equivalence.Lecture Notes in Mathematics 588 (1977). Zbl 0357.53022, 10.1007/BFb0091884 |
| Reference:
|
[13] A. Nijenhuis: Natural bundles and their general properties.Differential Geometry in Honour of K. Yano, Kino Kuniya, Toki 1972, 271-277. Zbl 0246.53018, MR 0380862 |
| Reference:
|
[14] J. F. Pommaret: Systems of Partial Differential Equations and Lie Pseudogroups.Math. and Its Аppl. 14 (1978); Russian transl. 1983. Zbl 0418.35028, MR 0731697 |
| Reference:
|
[15] A. A. Rodrigues, Ngo van Que: Troisième théorème fondamental de réalization de Cartan.Аnn. Inst. Fourier 25 (1975), 251-282. 10.5802/aif.551 |
| Reference:
|
[16] S. Sternberg: Lectures on Differential Geometry.Prentice Hall, New Јersey 1964. Zbl 0129.13102, MR 0193578 |
| Reference:
|
[17] V. V. Žarinov: On the Bäcklund correspondences.(in Russian). Matematičeskij sbornik 136 (1988), 274-291. |
| . |
