Loïc Foissy
Left ideals in an enveloping algebra, prelie products and applications to simple complex Lie algebras.
Thu, 01/07/2010 - 16:01 — SomNambulAuthors: Loïc Foissy
Subjects: Rings and Algebras
AbstractWe characterize prelie algebras in words of left ideals of the enveloping
algebras and in words of modules, and use this result to prove that a simple
complex finite-dimensional Lie algebra is not prelie, with the possible
exception of f4.Systems of Dyson-Schwinger equations.
Thu, 09/03/2009 - 17:38 — SomNambulAuthors: Loïc Foissy
Subjects: Rings and Algebras
AbstractWe consider systems of combinatorial Dyson-Schwinger equations (briefly,
SDSE) X_1=B^+_1(F_1(X_1,...,X_N))...X_N=B^+_N(F_N(X_1,...,X_N)) in the
Connes-Kreimer Hopf algebra H_I of rooted trees decorated by I={1,...,N},where
B^+_i is the operator of grafting on a root decorated by i, and F_1...,F_N are
non-constant formal series.The unique solution X=(X_1,...,X_N) of this equation
generates a graded subalgebra H_S of H_I. We characterize here all the families
of formal series (F_1,...,F_N) such that H_S is a Hopf subalgebra.
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