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

Kód výsledku v IS VaVaI

RIV/62690094:18470/20:50017270 - isvavai.cz

Výsledek na webu

http://www.mathjournals.org/mmj/2020-020-002/

DOI - Digital Object Identifier

10.17323/1609-4514-2020-20-2-217-256

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

GA18-00496S: Singulární prostory ze speciální holonomie a foliací

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

MOSCOW MATHEMATICAL JOURNAL

ISSN

1609-3321

e-ISSN

—

Svazek periodika

20

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

RU - Ruská federace

Počet stran výsledku

40

Strana od-do

217-256

Kód UT WoS článku

000526932000001

EID výsledku v databázi Scopus

2-s2.0-85084201169