2024 Hopf algebras topological recursion

Hopf algebras topological recursion

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August undefined, 2024

WebHopf Algebras and Topological Recursion JOÃO N. ESTEVES CAMGSD, Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisboa, … WebThe use of graphs, in particular of trees, binary trees and planar binary trees, in mathematical physics has a long tradition. The canonical examples are perhaps Feynman diagrams but the connection with Hopf Algebras of trees started with the works of Connes and Kreimer [6, 7, 8] that describe the combinatorics of the procedure of extracting sub …

Geometric And Topological Aspects Of Coxeter Groups And …

WebWe consider a model for topological recursion based on the Hopf Algebra of planar binary trees of Loday and Ronco. We show that extending this Hopf Algebra by identifying pairs of nearest neighbor leaves and thus producing graphs with loops we obtain the full recursion formula of Eynard and Orantin. Web26 aug. 2015 · Abstract We consider a model for topological recursion based on the Hopf Algebra of planar binary trees of Loday and Ronco. We show that extending this Hopf … shock pen ebay

Hopf Algebraic Structure for Tagged Graphs and Topological Recursion

Webtask dataset model metric name metric value global rank remove WebThe papers contained in the volume present a snapshot of rapid and rich developments in the emerging research field known as topological recursion. It has its origin around 2004 … WebHOPF ALGEBRAS AND TOPOLOGICAL RECURSION. João Esteves. Download Free PDF View PDF. FUNDAMENTOS E MÉTODOS DE RENORMALIZAÇÃO - IX ESCOLA CBPF 2012.pdf. Armando Flavio Rodrigues. Download Free PDF View PDF. Combinatorics and algebra of tensor calculus. 2015 • Xuexing Lu. rabun county vacation rentals

Modular tensor categories and topological field theories - uni …

Hopf Algebras and Topological Recursion - Semantic Scholar

WebHopf algebras are a relatively new concept in algebra, ﬁrst encountered by their namesake Heinz Hopf in 1941 in the ﬁeld of algebraic topology. In the 1960s, study of Hopf algebras increased, perhaps spurred by the ﬁndings of Moss Eisenberg Sweedler, and by the late 1980sandearly1990s ... Web2 r : H !A projection to a Hopf subalgebra, r(H) !B projection to a Hopf subalgebra B dual to A, then H-mod and r(H)-mod have equivalent categories of Yetter Drinfeld modules. (Barvels, Lentner, CS, 2015) and are even categorically Morita equivalent. Classical objects like Hopf algebras deserve to be studied by their bicategory of module ... rabun county votingWebintegrals admit a topological expansion, in certain cases, they enumerate discrete coloured surfaces of a given topology, while the well known Kontsevich integrals count … shock pen how it works

"Web1 okt. 2024 · There have been different general definitions of both Hopf algebras and H-spaces adopted across the literature. Algebraic topologists in particular are used to working with CW complexes and may brush over the finer points of the full theory to make their work more accessible, since they deal mainly with such a nice class of Hopf algebras. " - Hopf algebras topological recursion

Hopf algebras topological recursion

Web16 apr. 2024 · Advanced Topics in Algebra: Hopf algebras, quantum groups and Nichols algebras Thorsten Heidersdorf Universität Bonn SS 2024 Tuesday, 10.15 - 12.00 am, Friday 10.15 ... Content: Hopf algebras are certain bialgebras that occur naturally in many fields such as algebraic topology, representation theory and combinatorics. Webnotion of Hopf algebra such that also the above example, with an infinite group, Received by the editors September 25, 1992. ... that could be helpful in developing the topological theory. In a recent paper [6], we also showed that multiplier Hopf algebras, as …

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WebS: H!Hmaking Hinto a Hopf algebra. Proposition 2. If His a commutative or cocommutative Hopf algebra with antipode S, then S2= id H. Proposition 3. Let Hbe a Hopf algebra with antipode S, then for x2Hwith ( x) = 1+, ( x) = -. 1.6. Hopf Algebras and Combinatorics. Hopf algebra techniques in combinatorics were pioneered by WebLet Abe a Hopf algebra over a eld kwith counit ": A!kand antipode S: A!A. Tensor products will be over kunless otherwise speci ed. We will use Sweedler notation for the coproduct : A!A A, that is ( a) = P (a) a 1 a 2 for a2A, although we will often leave out the subscript (a) on the summation symbol.

Web6 feb. 2024 · MSC Classification Codes. 00-xx: General. 00-01: Instructional exposition (textbooks, tutorial papers, etc.) 00-02: Research exposition (monographs, survey articles ... WebHopf algebra is nice object full of structure (a bialgebra with an antipode). To get some idea what it looks like, group itself is a Hopf algebra, considered over a field with one element …

WebAn H-space consists of a topological space X, together with an element e of X and a continuous map μ : X × X → X, such that μ (e, e) = e and the maps x ↦ μ (x, e) and x ↦ μ (e, x) are both homotopic to the identity map through maps sending e to e. [2] WebLike a quantum group structure, its product is non-commutative. With the help of the Hopf algebraic structure, after taking account symmetry of the tagged graphs, we reconstruct the topological recursion on spectral curves proposed by B. Eynard and N. Orantin, which includes the one-loop equations of various matrix integrals as special cases.

Web18 sep. 2024 · We first review our previous work arxiv:1503.02993 [math-ph] where we considered a model for topological recursion based on the Hopf Algebra of planar …

Web13 sep. 2024 · Hopf algebras. Mathematics Lecture Note Series, 1969. Syllabus 1. The structure and action of Hopf algebras; 2. Integral theory; 3. Drinfeld double; 4. Quasi-Hopf algebras; 5. Tensor... rabun county voting locationWebWe characterize Frobenius algebras A as algebras having a comultiplication which is a map of A-modules. ... Topological recursion and geometry. Gaëtan Borot; 22 April 2024 Reviews in Mathematical Physics, Vol ... Generalized Frobenius Algebras and Hopf Algebras. Miodrag Cristian Iovanov. 20 November 2024 Canadian Journal of … rabun county vs jeff davis high foot allWeb21 sep. 2024 · Hopf algebras were first introduced in relation to the homology of groups and more generally of topological spaces equipped with a product. This chapter surveys some of the main applications of Hopf algebras in the field. The reader is assumed to have some familiarity with its fundamental notions. shock pen for painWeb27 jul. 2016 · Zhengzhou University of Light Industry We show that there exists a Hopf algebraic structure for the topological recursion on arbitrary algebraic curves proposed … rabun county vs pierce countyWeb3 aug. 2006 · The unification is given by a Birkhoff type decomposition that was obtained from the Baker–Campbell–Hausdorff formula in our study of the Hopf algebra approach … rabun county voting resultsWeb27 okt. 2024 · Just as an algebrais a monoidin Vectand a bialgebrais a bimonoidin VectVect, a Hopf algebra is a Hopf monoidin VectVect. Remark Caution: convention in topology In algebraic topology, it is common to define Hopf algebras without mentioning the antipode, since in many topological cases of interest it exists automatically. rabun county vs jeff davisWebHere Δ is the comultiplication of the bialgebra, ∇ its multiplication, η its unit and ε its counit. In the sumless Sweedler notation, this property can also be expressed as (()) = (()) = ().As for algebras, one can replace the underlying field K with a commutative ring R in the above definition.. The definition of Hopf algebra is self-dual (as reflected in the symmetry of the … rabun county water and sewer