Geodesic
Tree Diagram Lie Algebras of Differential Operators and Evolution Partial Differential Equations
Journal of Lie theory, Tome 16 (2006) no. 4, pp. 691-618.

Voir la notice de l'article provenant de la source Heldermann Verlag

A 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.
Classification : 17B30, 35F15, 35G15, 35C15, 35Q58
Mots-clés : Tree diagram, Lie algebra of differential operators, abelian ideal, evolution partial differential equation, Campbell-Hausdorff 
@article{JLT_2006_16_4_JLT_2006_16_4_a3,
     author = {X.-P. Xu },
     title = {Tree {Diagram} {Lie} {Algebras} of {Differential} {Operators} and {Evolution} {Partial} {Differential} {Equations}},
     journal = {Journal of Lie theory},
     pages = {691--618},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2006},
     url = {http://geodesic.mathdoc.fr/item/JLT_2006_16_4_JLT_2006_16_4_a3/}
}
TY  - JOUR
AU  - X.-P. Xu 
TI  - Tree Diagram Lie Algebras of Differential Operators and Evolution Partial Differential Equations
JO  - Journal of Lie theory
PY  - 2006
SP  - 691
EP  - 618
VL  - 16
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JLT_2006_16_4_JLT_2006_16_4_a3/
ID  - JLT_2006_16_4_JLT_2006_16_4_a3
ER  - 
%0 Journal Article
%A X.-P. Xu 
%T Tree Diagram Lie Algebras of Differential Operators and Evolution Partial Differential Equations
%J Journal of Lie theory
%D 2006
%P 691-618
%V 16
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JLT_2006_16_4_JLT_2006_16_4_a3/
%F JLT_2006_16_4_JLT_2006_16_4_a3
X.-P. Xu . Tree Diagram Lie Algebras of Differential Operators and Evolution Partial Differential Equations. Journal of Lie theory, Tome 16 (2006) no. 4, pp. 691-618. http://geodesic.mathdoc.fr/item/JLT_2006_16_4_JLT_2006_16_4_a3/