| Title:
|
Geometry of third order ODE systems (English) |
| Author:
|
Medvedev, Alexandr |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
46 |
| Issue:
|
5 |
| Year:
|
2010 |
| Pages:
|
351-361 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We compute cohomology spaces of Lie algebras that describe differential invariants of third order ordinary differential equations. We prove that the algebra of all differential invariants is generated by 2 tensorial invariants of order 2, one invariant of order 3 and one invariant of order 4. The main computational tool is a Serre-Hochschild spectral sequence and the representation theory of semisimple Lie algebras. We compute differential invariants up to degree 2 as application. (English) |
| Keyword:
|
geometry of ordinary differential equations |
| Keyword:
|
normal Cartan connections, cohomology of Lie algebras |
| MSC:
|
17B56 |
| MSC:
|
34A26 |
| MSC:
|
53B15 |
| idZBL:
|
Zbl 1249.34024 |
| idMR:
|
MR2753989 |
| . |
| Date available:
|
2010-12-14T15:07:43Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141389 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
