20 research outputs found
A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver
We show that there exists a morphism between a group
introduced by G. Wilson and a quotient of the group of tame symplectic
automorphisms of the path algebra of a quiver introduced by Bielawski and
Pidstrygach. The latter is known to act transitively on the phase space
of the Gibbons-Hermsen integrable system of rank 2, and we
prove that the subgroup generated by the image of
together with a particular tame symplectic automorphism has the property that,
for every pair of points of the regular and semisimple locus of
, the subgroup contains an element sending the first point
to the second
Insertion and Elimination Lie Algebra: the Ladder case
We prove that insertion-elimination Lie algebra of Feynman graphs, in the
ladder case, has a natural interpretation in terms of a certain algebra of
infinite dimensional matrices. We study some aspects of its representation
theory and we discuss some relations with the representation of the Heisenberg
algebraComment: LaTex, 17 pages, typos corrected, to appear in LM
Post-Lie Algebras and Isospectral Flows
In this paper we explore the Lie enveloping algebra of a post-Lie algebra
derived from a classical -matrix. An explicit exponential solution of the
corresponding Lie bracket flow is presented. It is based on the solution of a
post-Lie Magnus-type differential equation
The Structure of the Ladder Insertion-Elimination Lie algebra
We continue our investigation into the insertion-elimination Lie algebra of
Feynman graphs in the ladder case, emphasizing the structure of this Lie
algebra relevant for future applications in the study of Dyson-Schwinger
equations. We work out the relation of this Lie algebra to some classical
infinite dimensional Lie algebra and we determine its cohomology.Comment: 24 pages, LaTex, typos correcte