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Related papers: Some graphical aspects of Frobenius structures

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For a closed K\"{a}hler manifold with a Hamiltonian action of a connected compact Lie group by holomorphic isometries, we construct a formal Frobenius manifold structure on the equivariant cohomology by exploiting a natural DGBV algebra…

Differential Geometry · Mathematics 2007-05-23 Huai-Dong Cao , Jian Zhou

This paper studies Frobenius subalgebra posets in abelian monoidal categories and shows that, under general conditions--satisfied in all semisimple tensor categories over the complex field--they collapse to lattices through a rigidity…

Quantum Algebra · Mathematics 2025-10-27 Mainak Ghosh , Sebastien Palcoux

We show that a compact rigid balanced braided monoidal category with enough compact projective objects gives rise to a system of mapping class group representations compatible with the gluing along marked intervals. A motivation to consider…

Quantum Algebra · Mathematics 2026-02-24 Deniz Yeral

The goal of this note is to exhibit the integrability properties (in the sense of the Frobenius theorem) of holomorphic p-forms with values in certain line bundles with seminegative curvature on a compact Kaehler manifold. There are in fact…

Algebraic Geometry · Mathematics 2007-05-23 Jean-Pierre Demailly

We show that given a Frobenius algebra there is a unique notion of its second quantization, which is the sum over all symmetric group quotients of n--th tensor powers, where the quotients are given by symmetric group twisted Frobenius…

Algebraic Geometry · Mathematics 2009-11-07 Ralph M. Kaufmann

The theme of the paper is the use of commutative Frobenius algebras in braided strict monoidal categories in the study of varieties of circuits and communicating systems which occur in Computer Science, including circuits in which the wires…

Category Theory · Mathematics 2011-10-05 R. Rosebrugh , N. Sabadini , R. F. C. Walters

The aim of this paper is to show that there is a Hopf structure of the parabosonic and parafermionic algebras and this Hopf structure can generate the well known Hopf algebraic structure of the Lie algebras, through a realization of Lie…

Mathematical Physics · Physics 2015-06-26 C. Daskaloyannis , K. Kanakoglou , I. Tsohantjis

Based on the logarithmic algebraic geometry and the theory of Deligne systems, we define an abelian category of $\ell$-adic sheaves with weight filtrations on a logarithmic scheme over a finite field, which is similar to the category of…

Algebraic Geometry · Mathematics 2024-05-01 Kazuya Kato , Chikara Nakayama , Sampei Usui

We prove that the Nakayama automorphism of a Frobenius algebra acts trivially on the Hochschild cohomology of the algebra. As an application of this fact, we show how to construct certain invariants attached to such algebras, and to their…

K-Theory and Homology · Mathematics 2025-02-10 Mariano Suárez-Álvarez

We prove that the structure algebra of a Bruhat moment graph of a finite real root system is a Hopf algebroid with respect to the Hecke and the Weyl actions. We introduce new techniques (reconstruction and push-forward formula of a product,…

Algebraic Geometry · Mathematics 2023-03-07 Martina Lanini , Rui Xiong , Kirill Zainoulline

We explain the homological relation between the Frobenius structure on the deformation space of Calabi-Yau manifold and the gauge theory of Kodaira-Spencer gravity. We show that the genus zero generating function of descendant invariants on…

Quantum Algebra · Mathematics 2013-03-13 Si Li

We study Frobenius-Schur indicators of the regular representations of finite-dimensional semisimple Hopf algebras, especially group-theoretical ones. Those of various Hopf algebras are computed explicitly. In view of our computational…

Quantum Algebra · Mathematics 2010-10-21 Kenichi Shimizu

Submanifolds of Frobenius manifolds are studied. In particular, so-called natural submanifolds are defined and, for semi-simple Frobenius manifolds, classified. These carry the structure of a Frobenius algebra on each tangent space, but…

Differential Geometry · Mathematics 2020-12-15 I. A. B. Strachan

The purpose of this note is to relate certain ring-theoretic properties of rings in mixed and positive characteristics that are related to each other by a tilting operation used in perfectoid geometry. To this aim, we exploit the…

Commutative Algebra · Mathematics 2026-01-05 Kazufumi Eto , Jun Horiuchi , Kazuma Shimomoto

Two programs for the computation of perturbative expansions of quantum field theory amplitudes are provided. feyngen can be used to generate Feynman graphs for Yang-Mills, QED and $\varphi^k$ theories. Using dedicated graph theoretic tools…

High Energy Physics - Theory · Physics 2014-10-29 Michael Borinsky

We give some applications of a Hopf algebra constructed from a group acting on another Hopf algebra A as Hopf automorphisms, namely Molnar's smash coproduct Hopf algebra. We find connections between the exponent and Frobenius-Schur…

Representation Theory · Mathematics 2016-01-05 Susan Montgomery , Maria D. Vega , Sarah Witherspoon

We study a Hopf algebra $H$, which is finitely generated and projective over a commutative ring $k$, as a $P$-Frobenius algebra. We define modular functions in this setting, and provide a complete proof of Radford's formula for the fourth…

Rings and Algebras · Mathematics 2007-05-23 Lars Kadison , A. A. Stolin

The N-dimensional Cayley-Klein scheme allows the simultaneous description of $3^N$ geometries (symmetric orthogonal homogeneous spaces) by means of a set of Lie algebras depending on $N$ real parameters. We present here a quantum…

High Energy Physics - Theory · Physics 2019-07-19 A. Ballesteros , F. J. Herranz , M. A. del Olmo , M. Santander

This paper proposes a new, visual method to study numerical semigroups and the Frobenius problem. The method is based on building a so-called reduction graph, whose nodes usually correspond to monogenic semigroups, and whose edges can have…

Combinatorics · Mathematics 2018-09-05 Alexandru Pascadi

Carrier graphs of groups representing subgroups of a given relatively hyperbolic groups are introduced and a combination theorem for relatively quasi-convex subgroups is proven. Subsequently a theory of folds for such carrier graphs is…

Group Theory · Mathematics 2026-04-10 Richard Weidmann , Thomas Weller