Related papers: Algebraic Structures in local QFT
We summarize the Hopf algebra structure on Feynman diagrams and emphasize the interest in further algebraic structures hidden in Feynman graphs.
We introduce a notion of Hopf-Lie-Rinehart algebra and show that the universal algebra of a Hopf-Lie-Rinehart algebra acquires an ordinary Hopf algebra structure.
We study the structure of local algebras in relativistic conformal quantum field theory with phase boundaries. Phase boundaries are instances of a more general notion of boundaries that give rise to a variety of algebraic structures. These…
The holographic relation between local boundary conformal quantum field theories (BCFT) and their non-local boundary restrictions is reviewed, and non-vacuum BCFT's, whose existence was conjectured previously, are constructed.
In this work we study how to extend a partial action of a Hopf Algebra $A$ on an algebra $R$ to a partial action of a Hopf-Ore extension of $A$ on $R$. As consequence, we characterize all partial actions of rank one Hopf algebras (in…
Building on foundations introduced in a previous paper, we give several p-adic analytic descriptions of the categories of etale Zp-local systems and etale Qp-local systems on an affinoid algebra over a finite extension of Qp (or more…
We propose a new method to investigate the dimension of the space of integrals on a Hopf algebra $H$ and other properties of $H$-comodules.
We introduce and investigate using Hilbert modules the properties of the {\em Fourier algebra} $A(G)$ for a locally compact groupoid $G$. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This…
Family of doublings of Hopf algeras based on the product of algebra and its dual are constructed and studied. Special cases of these construction may be considered as natural quantum analogs of rings of differential operators on groups.…
We review the structures imposed on perturbative QFT by the fact that its Feynman diagrams provide Hopf and Lie algebras. We emphasize the role which the Hopf algebra plays in renormalization by providing the forest formulas. We exhibit how…
Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete…
We prove some results on the structure of certain classes of integral fusion categories and semisimple Hopf algebras under restrictions on the set of its irreducible degrees.
We give several characterizations of relative homological epimorphisms in the setting of locally convex topological algebras, thereby correcting a gap in our earlier paper [Trans. Moscow Math. Soc. 2008, 27-104].
We introduce general q-deformed multiple polylogarithms which even in the dilogarithm case differ slightly from the deformation usually discussed in the literature. The merit of the deformation as suggested, here, is that q-deformed…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
Cambrian trees are oriented and labeled trees which fulfill local conditions around each node generalizing the conditions for classical binary search trees. Based on the bijective correspondence between signed permutations and leveled…
The theory of integrals is used to analyse the structure of Hopf algebroids, introduced in math.QA/0302325. We prove that the total algebra of the Hopf algebroid is a separable extension of the base algebra if and only if it is a…
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…
If P, B, H are the algebras of the total space, the base space, and the structure group of a locally trivial principal fibre bundle (QPFB), left (right) gauge transformations are defined as automorphisms of the left (right) B-module P which…
We give a systematic description of the cyclic cohomology theory of Hopf algebroids in terms of its associated category of modules. Then we introduce a dual cyclic homology theory by applying cyclic duality to the underlying cocyclic…