| Title:
|
A note on Poisson derivations (English) |
| Author:
|
Li, Jiantao |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
68 |
| Issue:
|
3 |
| Year:
|
2018 |
| Pages:
|
657-660 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Free Poisson algebras are very closely connected with polynomial algebras, and the Poisson brackets are used to solve many problems in affine algebraic geometry. In this note, we study Poisson derivations on the symplectic Poisson algebra, and give a connection between the Jacobian conjecture with derivations on the symplectic Poisson algebra. (English) |
| Keyword:
|
Poisson algebra |
| Keyword:
|
derivation |
| Keyword:
|
Jacobian conjecture |
| MSC:
|
13N15 |
| MSC:
|
17B63 |
| idZBL:
|
Zbl 06986963 |
| idMR:
|
MR3851882 |
| DOI:
|
10.21136/CMJ.2017.0574-16 |
| . |
| Date available:
|
2018-08-09T13:10:31Z |
| Last updated:
|
2020-10-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147359 |
| . |
| Reference:
|
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| Reference:
|
[2] Makar-Limanov, L., Turusbekova, U., Umirbaev, U.: Automorphisms and derivations of free Poisson algebras in two variables.J. Algebra 322 (2009), 3318-3330. Zbl 1233.17016, MR 2567422, 10.1016/j.jalgebra.2008.01.005 |
| Reference:
|
[3] Makar-Limanov, L., Umirbaev, U.: Centralizers in free Poisson algebras.Proc. Amer. Math. Soc. 135 (2007), 1969-1975. Zbl 1158.17006, MR 2299468, 10.1090/S0002-9939-07-08678-9 |
| Reference:
|
[4] Makar-Limanov, L., Umirbaev, U.: The Freiheitssatz for Poisson algebras.J. Algebra 328 (2011), 495-503. Zbl 1285.17007, MR 2745580, 10.1016/j.jalgebra.2010.08.015 |
| Reference:
|
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| Reference:
|
[6] Shestakov, I. P., Umirbaev, U. U.: Poisson brackets and two-generated subalgebras of rings of polynomials.J. Am. Math. Soc. 17 (2004), 181-196. Zbl 1044.17014, MR 2015333, 10.1090/S0894-0347-03-00438-7 |
| Reference:
|
[7] Shestakov, I. P., Umirbaev, U. U.: The tame and the wild automorphisms of polynomial rings in three variables.J. Am. Math. Soc. 17 (2004), 197-227. Zbl 1056.14085, MR 2015334, 10.1090/S0894-0347-03-00440-5 |
| Reference:
|
[8] Umirbaev, U.: Universal enveloping algebras and universal derivations of Poisson algebras.J. Algebra 354 (2012), 77-94. Zbl 1270.17013, MR 2879224, 10.1016/j.jalgebra.2012.01.003 |
| Reference:
|
[9] Essen, A. van den: Polynomial Automorphisms and the Jacobian Conjecture.Progress in Mathematics 190, Birkhäuser, Basel (2000). Zbl 0962.14037, MR 1790619, 10.1007/978-3-0348-8440-2 |
| . |
