Related papers: Integrable Renormalization I: the Ladder Case
This paper introduces a Hopf algebra structure on a family of reduced pipe dreams. We show that this Hopf algebra is free and cofree, and construct a surjection onto a commutative Hopf algebra of permutations. The pipe dream Hopf algebra…
This is an introduction for algebraists to the theory of algebras and Hopf algebras in braided categories. Such objects generalise super-algebras and super-Hopf algebras, aswell as colour-Lie algebras. Basic facts about braided categories C…
We equip the graded polynomial algebra generated by nonplanar rooted binary trees with a Hopf algebra structure by defining a coproduct which disallows cutting both children of any given vertex, refining Connes-Kreimer's notion of…
In a previous paper by the author a universal ring of invariants for algebraic structures of a given type was constructed. This ring is a polynomial algebra that is generated by certain trace diagrams. It was shown that this ring admits the…
Typed decorated trees are used by Bruned, Hairer and Zambotti to give a description of a renormalisation processon stochastic PDEs. We here study the algebraic structures on these objects: multiple prelie algebrasand related operads…
We consider skew-commutative subalgebras in Drinfeld-Jimbo quantum groups at a root of unity $\zeta$ generated by primitive power elements. We classify the centrality and commutativity of these skew-polynomial algebras depending on the Lie…
We construct explicit Drinfel'd twists for the generalized Cartan type $H$ Lie algebras in characteristic $0$ and obtain the corresponding quantizations and their integral forms. Via making modular reductions including modulo $p$ reduction…
Following Manin's approach to renormalization in the theory of computation, we investigate Dyson-Schwinger equations on Hopf algebras, operads and properads of flow charts, as a way of encoding self-similarity structures in the theory of…
In this talk, we are concerned with the formulation and understanding of the combinatorics of time-ordered n-point functions in terms of the Hopf algebra of field operators. Mathematically, this problem can be formulated as one in…
We formulate the problem of finding the low-energy limit of spin foam models as a coarse-graining problem in the sense of statistical physics. This suggests that renormalization group methods may be used to find that limit. However, since…
The analysis of the combinatorics resulting from the perturbative expansion of the transition amplitude in quantum field theories, and the relation of this expansion to the Hausdorff series leads naturally to consider an infinite…
We begin by considering the graded vector space with a basis consisting of rooted trees, graded by the count of non-root vertices. We define two linear operators on this vector space, the growth and pruning operators, which respectively…
Three equivalent methods allow to compute the antipode of the Hopf algebras of Feynman diagrams in perturbative quantum field theory (QFT): the Dyson-Salam formula, the Bogoliubov formula, and the Zimmermann forest formula. Whereas the…
Using the standard filtration associated with a generalized lifting method, we determine all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose coradical generates a Hopf subalgebra isomorphic…
In this talk, we show how the Connes-Kreimer Hopf algebra morphism can be extended when taking into account the wave-function renormalization. This leads us to a semi-direct product of invertible power series by formal diffeomorphisms.
For a given finite dimensional Hopf algebra $H$ we describe the set of all equivalence classes of cocycle deformations of $H$ as an affine variety, using methods of geometric invariant theory. We show how our results specialize to the…
Let A be a Hopf algebra and H a coalgebra. We shall describe and classify up to an isomorphism all Hopf algebras E that factorize through A and H: that is E is a Hopf algebra such that A is a Hopf subalgebra of E, H is a subcoalgebra in E…
We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions which was recently studied as a vector space by Rosas and Sagan. The bases for this algebra are indexed by set partitions. We show that there…
We give a natural monomorphism from the necklace Lie coalgebra, defined for any quiver, to Connes and Kreimer's Lie coalgebra of trees, and extend this to a map from a certain quiver-theoretic Hopf algebra to Connes and Kreimer's…
Nichols algebras naturally appear in the classification of finite dimensional pointed Hopf algebras. Assuming only that the base field has characteristic zero several new finite dimensional rank 2 Nichols algebras of diagonal type are…