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Various local global principles for abelian groups.

George Peschke, Peter Symonds (1994)

Publicacions Matemàtiques

We discuss local global principles for abelian groups by examining the adjoint functor pair obtained by (left adjoint) sending an abelian group A to the local diagram L(A) = {Z(p) ⊗ A → Q ⊗ A} and (right adjoint) applying the inverse limit functor to such diagrams; p runs through all integer primes. We show that the natural map A → lim L(A) is an isomorphism if A has torsion at only finitely many primes. If A is fixed we answer the genus problem of identifying all those groups B for which the local...

Vector invariant ideals of abelian group algebras under the actions of the unitary groups and orthogonal groups

Lingli Zeng, Jizhu Nan (2016)

Czechoslovak Mathematical Journal

Let F be a finite field of characteristic p and K a field which contains a primitive p th root of unity and char K ≠ p . Suppose that a classical group G acts on the F -vector space V . Then it can induce the actions on the vector space V ⊕ V and on the group algebra K [ V ⊕ V ] , respectively. In this paper we determine the structure of G -invariant ideals of the group algebra K [ V ⊕ V ] , and establish the relationship between the invariant ideals of K [ V ] and the vector invariant ideals of K [ V ⊕ V ] , if G is a unitary group or orthogonal group....

Veech Groups of Loch Ness Monsters

Piotr Przytycki, Gabriela Schmithüsen, Ferrán Valdez (2011)

Annales de l’institut Fourier

We classify Veech groups of tame non-compact flat surfaces. In particular we prove that all countable subgroups of G L + ( 2 , R ) avoiding the set of mappings of norm less than 1 appear as Veech groups of tame non-compact flat surfaces which are Loch Ness monsters. Conversely, a Veech group of any tame flat surface is either countable, or one of three specific types.

Veränderungen über einen Satz von Timmesfeld – I. Quadratic Actions

Adrien Deloro (2013)

Confluentes Mathematici

We classify quadratic SL 2 ( 𝕂 ) - and 𝔰𝔩 2 ( 𝕂 ) -modules by crude computation, generalising in the first case a Theorem proved independently by F.G. Timmesfeld and S. Smith. The paper is the first of a series dealing with linearisation results for abstract modules of algebraic groups and associated Lie rings.

Violations of the Ingleton inequality and revising the four-atom conjecture

Nigel Boston, Ting-Ting Nan (2020)

Kybernetika

The entropy region is a fundamental object of study in mathematics, statistics, and information theory. On the one hand, it involves pure group theory, governing inequalities satisfied by subgroup indices, whereas on the other hand, computing network coding capacities amounts to a convex optimization over this region. In the case of four random variables, the points in the region that satisfy the Ingleton inequality (corresponding to abelian groups and to linear network codes) form a well-understood...

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