NDLI: The variational Poisson cohomology

Please wait, while we are loading the content...

The variational Poisson cohomology

Content Provider	Springer Nature Link
Author	De Sole, Alberto Kac, Victor G.
Copyright Year	2013
Abstract	It is well known that the validity of the so called Lenard–Magri scheme of integrability of a bi-Hamiltonian PDE can be established if one has some precise information on the corresponding 1st variational Poisson cohomology for one of the two Hamiltonian operators. In the first part of the paper we explain how to introduce various cohomology complexes, including Lie superalgebra and Poisson cohomology complexes, and basic and reduced Lie conformal algebra and Poisson vertex algebra cohomology complexes, by making use of the corresponding universal Lie superalgebra or Lie conformal superalgebra. The most relevant are certain subcomplexes of the basic and reduced Poisson vertex algebra cohomology complexes, which we identify (non-canonically) with the generalized de Rham complex and the generalized variational complex. In the second part of the paper we compute the cohomology of the generalized de Rham complex, and, via a detailed study of the long exact sequence, we compute the cohomology of the generalized variational complex for any quasiconstant coefficient Hamiltonian operator with invertible leading coefficient. For the latter we use some differential linear algebra developed in the Appendix.
Starting Page	1
Ending Page	145
Page Count	145
File Format	PDF
ISSN	02892316
Journal	Japanese Journal of Mathematics
Volume Number	8
Issue Number	1
e-ISSN	18613624
Language	English
Publisher	Springer Japan
Publisher Date	2013-03-20
Publisher Place	Japan
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	bi-Hamiltonian PDE Lie conformal algebra Poisson vertex algebra universal Lie superalgebra and Lie conformal superalgebra generalized variational complex variational polyvector field basic and variational Poisson cohomology linearly closed differential field Applications to integrable systems Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies Vertex operators; vertex operator algebras and related structures Relations with infinite-dimensional Lie algebras and other algebraic structures Cohomology of Lie (super)algebras Mathematics History of Mathematical Sciences
Content Type	Text
Resource Type	Article
Subject	Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Non-local Poisson structures and applications to the theory of integrable systems

Classical double, R-operators and negative flows of integrable hierarchies

The variational Poisson cohomology

Essential variational Poisson cohomology

On integrability of some bi-Hamiltonian two field systems of PDE

Loop algebras and bi-integrable couplings

Adler-Oevel-Ragnisco type operators and Poisson vertex algebras

Reduction Groups and Automorphic Lie Algebras

Mutation-Periodic Quivers, Integrable Maps and Associated Poisson Algebras

The variational Poisson cohomology

Similar Documents

Non-local Poisson structures and applications to the theory of integrable systems

Classical double, R-operators and negative flows of integrable hierarchies

The variational Poisson cohomology

Essential variational Poisson cohomology

On integrability of some bi-Hamiltonian two field systems of PDE

Loop algebras and bi-integrable couplings

Adler-Oevel-Ragnisco type operators and Poisson vertex algebras

Reduction Groups and Automorphic Lie Algebras

Mutation-Periodic Quivers, Integrable Maps and Associated Poisson Algebras

The variational Poisson cohomology