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1.
In this paper, we introduce a Frobenius Painlevé IV equation and the corresponding Hamilton system, and we give the symmetric form of the Frobenius Painlevé IV equation. Then, we construct the Lax pair of the Frobenius Painlevé IV equation. Furthermore, we recall the Frobenius modified KP hierarchy and the Frobenius KP hierarchy by bilinear equations, then we show how to get Frobenius Painlevé IV equation from the Frobenius modified KP hierarchy. In order to study the different aspects of the Frobenius Painlevé IV equation, we give the similarity reduction and affine Weyl group symmetry of the equation. Similarly, we introduce a Frobenius Painlevé II equation and show the connection between the Frobenius modified KP hierarchy and the Frobenius Painlevé II equation. 相似文献
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Following the approach of Carlet et al. (2011) [9], we construct a class of infinite-dimensional Frobenius manifolds underlying the Toda lattice hierarchy, which are defined on the space of pairs of meromorphic functions with possibly higher-order poles at the origin and at infinity. We also show a connection between these infinite-dimensional Frobenius manifolds and the finite-dimensional Frobenius manifolds on the orbit space of extended affine Weyl groups of type A defined by Dubrovin and Zhang. 相似文献
5.
Taekyun Kim 《Journal of Number Theory》2012,132(12):2854-2865
In this paper we consider non-linear differential equations which are closely related to the generating functions of Frobenius–Euler polynomials. From our non-linear differential equations, we derive some new identities between the sums of products of Frobenius–Euler polynomials and Frobenius–Euler polynomials of higher order. 相似文献
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Xiao-Wu Chen 《Mathematische Zeitschrift》2012,270(1-2):43-58
This paper consists of three results on Frobenius categories: (1) we give sufficient conditions on when a factor category of a Frobenius category is still a Frobenius category; (2) we show that any Frobenius category is equivalent to an extension-closed exact subcategory of the Frobenius category formed by Cohen–Macaulay modules over some additive category; this is an analogue of Gabriel–Quillen’s embedding theorem for Frobenius categories; (3) we show that under certain conditions an exact category with enough projective and enough injective objects allows a natural new exact structure, with which the given category becomes a Frobenius category. Several applications of the results are discussed. 相似文献
8.
Roberto Avanzi Waldyr Dias BenitsJr Steven D. Galbraith James McKee 《Designs, Codes and Cryptography》2011,61(1):71-89
Frobenius expansions are representations of integers to an algebraic base which are sometimes useful for efficient (hyper)elliptic
curve cryptography. The normal form of a Frobenius expansion is the polynomial with integer coefficients obtained by reducing
a Frobenius expansion modulo the characteristic polynomial of Frobenius. We consider the distribution of the coefficients
of reductions of Frobenius expansions and non-adjacent forms of Frobenius expansions (NAFs) to normal form. We give asymptotic
bounds on the coefficients which improve on naive bounds, for both genus one and genus two. We also discuss the non-uniformity
of the distribution of the coefficients (assuming a uniform distribution for Frobenius expansions). 相似文献
9.
《Journal of Pure and Applied Algebra》2022,226(12):107136
We adapt a construction due to Troesch to the category of strict polynomial superfunctors in order to construct complexes of injective objects whose cohomology is isomorphic to Frobenius twists of the (super)symmetric power functors. We apply these complexes to construct injective resolutions of the even and odd Frobenius twist functors, to investigate the structure of the Yoneda algebra of the Frobenius twist functor, and to compute other extension groups between strict polynomial superfunctors. By an equivalence of categories, this also provides cohomology calculations in the category of left modules over Schur superalgebras. 相似文献
10.
Some equivalent conditions for double Frobenius algebras to be strict ones are given. Then some examples of (strict or non-strict) double Frobenius algebras are presented. Finally, a sufficient and necessary condition for the trivial extension of a double Frobenius algebra to be a (strict) double Frobenius algebra is given. 相似文献
11.
林洁珠 《数学物理学报(B辑英文版)》2010,30(3):873-889
I.A.B. Strachan introduced the notion of a natural Frobenius submanifold of a Frobenius manifold and gave a sufficient but not necessary condition for a submanifold to be a natural Frobenius submanifold. This article will give a necessary and sufficient condition and classify the natural Frobenius hypersurfaces. 相似文献
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Chris Bernhardt 《Journal of Difference Equations and Applications》2016,22(1):55-66
The goal of this paper is to describe the connections between Perron–Frobenius theory and vertex maps on graphs. In particular, it is shown how Perron–Frobenius theory gives results about the sets of integers that can arise as periods of periodic orbits, about the concepts of transitivity and topological mixing and about horseshoes and topological entropy. 相似文献
13.
Daniel S. Sage 《代数通讯》2017,45(1):9-16
Classically, the exponent of a group is the least common multiple of the orders of its elements. This notion was generalized by Etingof and Gelaki to Hopf algebras. Kashina, Sommerhäuser, and Zhu later observed that there is a strong connection between exponents and Frobenius–Schur indicators. In this article, we introduce the notion of twisted exponents and show there is a similar relationship between the twisted exponent and the twisted Frobenius–Schur indicators defined in previous work of the authors. In particular, we exhibit a new formula for the twisted indicators and use it to prove periodicity and rationality statements. 相似文献
14.
Mohssin Zarouali-Darkaoui 《代数通讯》2013,41(2):689-724
We investigate adjoint and Frobenius pairs between categories of comodules over rather general corings. We particularize to the case of the adjoint pair of functors associated to a morphism of corings over different base rings, which leads to a reasonable notion of Frobenius coring extension. When applied to corings stemming from entwining structures, we obtain new results in this setting and in graded ring theory. 相似文献
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We show that the theory of Frobenius fields is decidable. This is conjectured in [4], [8] and [13], and we prove it by solving
a group theoretic problem to which this question is reduced there. To do this we present and develop the notion of embedding
covers of finite and pro-finite groups. We also answer two other problems from [8], again by solving a corresponding group
theoretic problem: A finite extension of a Frobenius field need not be Frobenius and there are PAC fields which are not Frobenius
fields.
Portions of this work will be incorporated in the doctoral dissertation of the first author done in Tel Aviv University under
the supervision of Prof. Moshe Jarden. 相似文献
16.
Ichiro Shimada 《Finite Fields and Their Applications》2012,18(2):337-361
We define Frobenius incidence varieties by means of the incidence relation of Frobenius images of linear subspaces in a fixed vector space over a finite field, and investigate their properties such as supersingularity, Betti numbers and unirationality. These varieties are variants of the Deligne–Lusztig varieties. We then study the lattices associated with algebraic cycles on them. We obtain a positive-definite lattice of rank 84 that yields a dense sphere packing from a 4-dimensional Frobenius incidence variety in characteristic 2. 相似文献
17.
Let X be a projective curve of genus 2 over an algebraically closed field of characteristic 2. The Frobenius map on X induces a rational map on the moduli scheme of rank-2 bundles. We show that up to isomorphism, there is only one (up to tensoring by an order two line bundle) semi-stable vector bundle of rank 2 (with determinant equal to a theta characteristic) whose Frobenius pull-back is not semi-stable. The indeterminacy of the Frobenius map at this point can be resolved by introducing Higgs bundles. 相似文献
18.
This paper is devoted to study Frobenius Poisson algebras. We introduce pseudo-unimodular Poisson algebras by generalizing unimodular Poisson algebras, and investigate Batalin-Vilkovisky structures on their cohomology algebras. For any Frobenius Poisson algebra, all Eatalin-Vilkovisky opera tors on its Poisson cochain complex are described explicitly. It is proved that there exists a Batalin-Vilkovisky operator on its cohomology algebra which is induced from a Batalin-Vilkovisky operator on the Poisson cochain complex, if and only if the Poisson st rue ture is pseudo-unimodular. The relation bet ween modular derivations of polynomial Poisson algebras and those of their truncated Poisson algebras is also described in some cases. 相似文献
19.
Every finite dimensional Hopf algebra is a Frobenius algebra, with Frobenius homomorphism given by an integral. The Nakayama automorphism determined by it yields a decomposition with degrees in a cyclic group. For a family of pointed Hopf algebras, we determine necessary and sufficient conditions for this decomposition to be strongly graded. 相似文献
20.
We study codes over Frobenius rings. We describe Frobenius rings via an isomorphism to the product of local Frobenius rings
and use this decomposition to describe an analog of linear independence. Special attention is given to codes over principal
ideal rings and a basis for codes over principal ideal rings is defined. We prove that a basis exists for any code over a
principal ideal ring and that any two basis have the same number of vectors.
Hongwei Liu is supported by the National Natural Science Foundation of China (10571067). 相似文献