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Galois module structure of the rings of integers in wildly ramified extensions

Stephen M. J. Wilson (1989)

Annales de l'institut Fourier

The main results of this paper may be loosely stated as follows.Theorem.— Let N and N ' be sums of Galois algebras with group Γ over algebraic number fields. Suppose that N and N ' have the same dimension and that they are identical at their wildly ramified primes. Then (writing 𝒪 N for the maximal order in N ) 𝒪 N 𝒪 N Γ Γ 𝒪 N ' 𝒪 N ' Γ . In many cases 𝒪 N Γ 𝒪 N ' . The role played by the root numbers of N and N ' at the symplectic characters of Γ in determining the relationship between the Γ -modules 𝒪 N and 𝒪 N ' is described. The theorem includes...

Generalized holomorphic analytic torsion

José Ignacio Burgos Gil, Gerard Freixas i Montplet, Răzvan Liţcanu (2014)

Journal of the European Mathematical Society

In this paper we extend the holomorphic analytic torsion classes of Bismut and Köhler to arbitrary projective morphisms between smooth algebraic complex varieties. To this end, we propose an axiomatic definition and give a classification of the theories of generalized holomorphic analytic torsion classes for projective morphisms. The extension of the holomorphic analytic torsion classes of Bismut and Köhler is obtained as the theory of generalized analytic torsion classes associated to R = 2 , R being...

Grothendieck ring of quantum double of finite groups

Jingcheng Dong (2010)

Czechoslovak Mathematical Journal

Let k G be a group algebra, and D ( k G ) its quantum double. We first prove that the structure of the Grothendieck ring of D ( k G ) can be induced from the Grothendieck ring of centralizers of representatives of conjugate classes of G . As a special case, we then give an application to the group algebra k D n , where k is a field of characteristic 2 and D n is a dihedral group of order 2 n .

Heisenberg algebra and a graphical calculus

Mikhail Khovanov (2014)

Fundamenta Mathematicae

A new calculus of planar diagrams involving diagrammatics for biadjoint functors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose Grothendieck ring contains an integral form of the Heisenberg algebra in infinitely many variables. We construct bases of the vector spaces of morphisms between products of generating objects in this category.

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