Tree Diagram Lie Algebras of Differential Operators and Evolution Partial Differential Equations

Simple item page
dc.creatorXu, Xiaoping
dc.date2007-06-28
dc.date.accessioned2026-07-07T08:13:04Z
dc.date.available2026-07-07T08:13:04Z
dc.descriptionA tree diagram is a tree with positive integral weight on each edge, which is a notion generalized from the Dynkin diagrams of finite-dimensional simple Lie algebras. We introduce two nilpotent Lie algebras and their extended solvable Lie algebras associated with each tree diagram. The solvable tree diagram Lie algebras turn out to be complete Lie algebras of maximal rank analogous to the Borel subalgebras of finite-dimensional simple Lie algebras. Their abelian ideals are completely determined. Using a high-order Campbell-Hausdorff formula and certain abelian ideals of the tree diagram Lie algebras, we solve the initial value problem of first-order evolution partial differential equations associated with nilpotent tree diagram Lie algebras and high-order evolution partial differential equations, including heat conduction type equations related to generalized Tricomi operators associated with trees.
dc.description31pages
dc.identifierhttps://arxiv.org/abs/0706.4201
dc.identifierhttp://arxiv.org/abs/0706.4201
dc.identifierJournal of Lie Theory, Vol 16 (2006), 691-718
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132669
dc.subjectRepresentation Theory
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subjectExactly Solvable and Integrable Systems
dc.titleTree Diagram Lie Algebras of Differential Operators and Evolution Partial Differential Equations
dc.typetext

Files

Collections

arXiv