MacWilliams’ equivalence theorem states that Hamming isometries between linear codes extend to monomial transformations of the ambient space. One of the most elegant proofs for this result is due to K. P. Bogart et al. (1978, Inform. and Control 37, 19–22) where the invertibility of orthogonality matrices of finite vector spaces is the key step. The present paper revisits this technique in orde...

Frobenius bimodules are connected with Frobenius algebras and extensions. For instance, a ring extension φ : R → S is a Frobenius extension if and only if RSS is a Frobenius bimodule [1]. Brzeziński and Gómez-Torrecillas studied in [4] certain properties of comatrix corings in relation to properties of bimodules. In particular they showed that the comatrix coring [6] induced by any Frobenius bi...

Let C be a smooth curve, and Mr(C) the coarse moduli space of vector bundles of rank r and trivial determinant on C. We examine the generalized Verschiebung map Vr : Mr(C) 99K Mr(C) induced by pulling back under Frobenius. Our main result is a computation of the degree of V2 for a general C of genus 2, in characteristic p > 2. We also give several general background results on the Verschiebung ...

This paper develops a compositional vector-based semantics of subject and object relative pronouns within a categorical framework. Frobenius algebras are used to formalise the operations required to model the semantics of relative pronouns, including passing information between the relative clause and the modified noun phrase, as well as copying, combining, and discarding parts of the relative ...

‎the frobenius complement of a given frobenius group acts on its kernel‎. ‎the scheme which is arisen from the orbitals of this action is called ferrero pair scheme‎. ‎in this paper‎, ‎we show that the fibers of a ferrero pair scheme consist of exactly one singleton fiber and every two fibers with more than one point have the same cardinality‎. ‎moreover‎, ‎it is shown that the restriction of a...

We study regular non-semisimple Dubrovin-Frobenius manifolds in dimensions 2,3,4. focus on the case where Jordan canonical form of operator multiplication by Euler vector field has a single block. Our results rely existence special local coordinates introduced [4] for flat F-manifolds with field. In such invariant metric manifold takes which is starting point our construction.

This paper develops a compositional vector-based semantics of relative pronouns within a categorical framework. Frobenius algebras are used to formalise the operations required to model the semantics of relative pronouns, including passing information between the relative clause and the modified noun phrase, as well as copying, combining, and discarding parts of the relative clause. We develop ...

We consider a subclass of the class of group-theoretical fusion categories: To every finite group G and subgroup H one can associate the category of G-graded vector spaces with a two-sided H-action compatible with the grading. We derive a formula that computes higher Frobenius-Schur indicators for the objects in such a category using the combinatorics and representation theory of the groups inv...

Let X be a smooth projective variety of dimension n over an algebraically closed field k with char(k) = p > 0 and F : X → X1 be the relative Frobenius morphism. For any vector bundle W on X , we prove that instability of F∗W is bounded by instability of W ⊗ T(Ω X ) (0 ≤ l ≤ n(p − 1))(Corollary 4.8). When X is a smooth projective curve of genus g ≥ 2, it implies F∗W being stable whenever W is st...

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–Macaulaymodules over some additive category; this is an analogue of Gabriel–Quillen’...