Geodesic
On formal theory of differential equations. III
Mathematica Bohemica, Tome 116 (1991) no. 1, pp. 60-90

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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.
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.
DOI : 10.21136/MB.1991.126196
Classification : 22E65, 35A30, 58A17, 58H05
Keywords: Lie-Cartan pseudogroups; diffieties; equivalence problem; Cauchy characteristics; composition series; geometrical object 
Chrastina, Jan. On formal theory of differential equations. III. Mathematica Bohemica, Tome 116 (1991) no. 1, pp. 60-90. doi: 10.21136/MB.1991.126196
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[1] E. Cartan: Oeuvres complètes II. 2. Paris 1953. | MR

[2] E. Cartan: Oeuvres complète II. 2. Paris 1953.

[3] J. Chrastina: On formal theory of differential equations I. Časopis pěst. mat. 111 (1986), 353-383. | MR | Zbl

[4] J. Chrastina: On formal theory of differential equations II. Časopis pěst. mat. 114 (1989) 60-105. | MR | Zbl

[5] J. Chrastina: From elementary algebra to Bäcklund transformations. Czechoslovak Math. J. 40 (1990), 239-257. | MR | Zbl

[6] H. Goldschmidt D. Spencer: On non-linear cohomology of Lie equations I. Acta Math. 136 (1976), 103-170. | DOI | MR

[7] V. W. Guillemin S. Sternberg: An algebraic model of transitive differential geometry. Bull. Amer. Math. Soc. 70 (1946), 16-47. | MR

[8] V. W. Guillemin S. Sternberg: The Lewy counterexample and the local equivalence problem for G-structures. J. Diff. Geom. 1 (1967), 127-131. | DOI | MR

[9] T. Higa: On the isomorphic reduction of an invariant associated with a Lie pseudogroup. Comm. Math. Univ. Sancti Pauli 34 (1985), 163-175. | MR | Zbl

[10] V. G. Kac: Simple irreducible graded Lie algebras of finite growth. (in Russian). Izvěstija Akad. Nauk 32 (1968), 1323-1367. | MR | Zbl

[11] S. Lie: Die Grundlagen für die Theorie der unendlichen kontinuierlichen Transformationsgruppen. Ges. Abh. 6, Leipzig 1927, 310-364.

[12] P. Molino: Théorie des G-structures, le problème d'equivalence. Lecture Notes in Mathematics 588 (1977). | DOI | Zbl

[13] A. Nijenhuis: Natural bundles and their general properties. Differential Geometry in Honour of K. Yano, Kino Kuniya, Toki 1972, 271-277. | MR | Zbl

[14] J. F. Pommaret: Systems of Partial Differential Equations and Lie Pseudogroups. Math. and Its Аppl. 14 (1978); Russian transl. 1983. | MR | Zbl

[15] A. A. Rodrigues, Ngo van Que: Troisième théorème fondamental de réalization de Cartan. Аnn. Inst. Fourier 25 (1975), 251-282. | DOI

[16] S. Sternberg: Lectures on Differential Geometry. Prentice Hall, New Јersey 1964. | MR | Zbl

[17] V. V. Žarinov: On the Bäcklund correspondences. (in Russian). Matematičeskij sbornik 136 (1988), 274-291.

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