Results 11 to 20 of about 24,029 (191)

Second quantized Frobenius algebras [PDF]

Communications in Mathematical Physics, 2003
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 algebras.
Adem, Atiyah, Batyrev, Dijkgraaf, Fantechi, Kaufmann, Kaufmann, Lehn, Ralph M. Kaufmann, Satake, Toen, Wang   +11 more
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Interacting Frobenius Algebras are Hopf [PDF]

Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, 2016
Theories featuring the interaction between a Frobenius algebra and a Hopf algebra have recently appeared in several areas in computer science: concurrent programming, control theory, and quantum computing, among others.
Abramsky Samson, Backens Miriam, Backens Miriam, Coecke Bob, Duncan Ross, Duncan Ross, Edwards William, Fauser Bertfried, Lack Stephen, R. Street. Quantum Groups, Rosebrugh R., Sadrzadeh Mehrnoosh, Selinger P., Selinger Peter, Sobociński Paweł   +14 more
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Twin TQFTs and Frobenius Algebras [PDF]

Journal of Mathematics, 2013
We introduce the category of singular 2-dimensional cobordisms and show that it admits a completely algebraic description as the free symmetric monoidal category on a twin Frobenius algebra, by providing a description of this category in terms of ...
Carmen Caprau
doaj   +3 more sources

Frobenius nil-Hecke algebras [PDF]

Pacific Journal of Mathematics, 2021
To any Frobenius superalgebra $A$ we associate towers of Frobenius nilCoxeter algebras and Frobenius nilHecke algebras. These act naturally, via Frobenius divided difference operators, on Frobenius polynomial algebras. When $A$ is the ground ring, our algebras recover the classical nilCoxeter and nilHecke algebras.
Savage, Alistair, Stuart, John
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Nearly Frobenius algebras [PDF]

European Journal of Mathematics, 2019
In this introductory paper we study nearly Frobenius algebras which are generalizations of the concept of a Frobenius algebra which appear naturally in topology: nearly Frobenius algebras have no traces (co-units). We survey the most basic foundational results and some of the applications they encounter in geometry, topology and representation theory.
Ana González, Ernesto Lupercio, Carlos Segovia, Bernardo Uribe   +3 more
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Nearly Frobenius dimension of Frobenius algebras

Communications in Algebra, 2022
This article is divided into two parts. In the first part we work over a field $\mathbb{k}$ and prove that the Frobenius space associated to a Frobenius algebra is generated as left A-module by the Frobenius coproduct. In particular, we prove that the Frobenius dimension coincides with the dimension of the algebra.
Dalia Artenstein, Ana González, Gustavo Mata   +2 more
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Constructing Nearly Frobenius Algebras [PDF]

Algebras and Representation Theory, 2014
In the first part we study nearly Frobenius algebras. The concept of nearly Frobenius algebras is a generalization of the concept of Frobenius algebras. Nearly Frobenius algebras do not have traces, nor they are self-dual. We prove that the known constructions: direct sums, tensor, quotient of nearly Frobenius algebras admit natural nearly Frobenius ...
Artenstein, Dalia, González, Ana, Lanzilotta, Marcelo   +2 more
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Orbifolding Frobenius Algebras [PDF]

International Journal of Mathematics, 2003
We study the general theory of Frobenius algebras with group actions. These structures arise when one is studying the algebraic structures associated to a geometry stemming from a physical theory with a global finite gauge group, i.e. orbifold theories. In this context, we introduce and axiomatize these algebras.
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Algebraic classical W-algebras and Frobenius manifolds [PDF]

Letters in Mathematical Physics, 2021
We consider Drinfeld-Sokolov bihamiltonian structure associated to a distinguished nilpotent elements of semisimple type and the space of common equilibrium points defined by its leading term. On this space, we construct a local bihamiltonian structure which form an exact Poisson pencil, defines an algebraic classical $W$-algebra, admits a ...
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Frobenius rational loop algebra [PDF]

manuscripta mathematica, 2007
Recently R. Cohen and V. Godin have proved that the homology of the free loop space of a closed oriented manifold with coefficients in a field has the structure of a Frobenius algebra without counit. In this short note we prove that when the characteristic of the field is zero and when the manifold is 1-connected the algebraic structure depends only on
Chataur, David, Thomas, Jean-Claude
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