HOMOGENEOUS SYMPLECTIC 4-MANIFOLDS AND FINITE DIMENSIONAL LIE ALGEBRAS OF SYMPLECTIC VECTOR FIELDS ON THE SYMPLECTIC 4-SPACE

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50017270" target="_blank" >RIV/62690094:18470/20:50017270 - isvavai.cz</a>
Result on the web
<a href="http://www.mathjournals.org/mmj/2020-020-002/" target="_blank" >http://www.mathjournals.org/mmj/2020-020-002/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.17323/1609-4514-2020-20-2-217-256" target="_blank" >10.17323/1609-4514-2020-20-2-217-256</a>

Result language
angličtina
Original language name
HOMOGENEOUS SYMPLECTIC 4-MANIFOLDS AND FINITE DIMENSIONAL LIE ALGEBRAS OF SYMPLECTIC VECTOR FIELDS ON THE SYMPLECTIC 4-SPACE
Original language description
We classify the finite type (in the sense of E. Cartan theory of prolongations) subalgebras h subset of sp(V), where V is the symplectic 4-dimensional space, and show that they satisfy h((k)) = 0 for all k > 0. Using this result, we reduce the problem of classification of graded transitive finite-dimensional Lie algebras g of symplectic vector fields on V to the description of graded transitive finite-dimensional subalgebras of the full prolongations p(1)((infinity)) and p(2)((infinity)), where p(1) and p(2) are the maximal parabolic subalgebras of sp(V). We then classify all such g subset of p(i)((infinity)), i = 1; 2, under some assumptions, and describe the associated 4-dimensional homogeneous symplectic manifolds (M = G/K, omega). We prove that any reductive homogeneous symplectic manifold (of any dimension) admits an invariant torsion free symplectic connection, i.e., it is a homogeneous Fedosov manifold, and give conditions for the uniqueness of the Fedosov structure. Finally, we show that any nilpotent symplectic Lie group (of any dimension) admits a natural invariant Fedosov structure which is Ricci-flat.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA18-00496S" target="_blank" >GA18-00496S: Singular spaces from special holonomy and foliations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)