Abstract. Let G be the semidirect product A1 ⋉ A of the adeles and the norm 1 ideles. Let Γ be the discrete subgroup Q× ⋉Q. In this paper the trace formula for this setting is established and used to give the complete decomposition of the G-representation on L2(Γ\G). It turns out that every character of the norm-1 idele class group gives a one dimensional isotype and the complement of those con...

We prove that the bicrossed product of two groups is a quotient of the pushout of two semidirect products. A matched pair of groups (H,G,α, β) is deformed using a combinatorial datum (σ, v, r) consisting of an automorphism σ of H , a permutation v of the set G and a transition map r : G → H in order to obtain a new matched pair `

This paper deals with sufficiency conditions for irreducibility of certain induced modules. We also construct irreducible representations for a group G over a field K where the group G is a semidirect product of a normal abelian subgroup N and a subgroup H. The main results are proved with the assumption that charK does not divide |G| but there is no assumption made of K being algebraically clo...

In a previous paper, the authors introduced and characterized a new kind of matrices called {K,s+1}-potent. In this paper, an associated group to a {K, s+1}-potent matrix is explicitly constructed and its properties are studied. Moreover, it is shown that the group is a semidirect product of Z2 acting on Z(s+1)2−1. For some values of s, more specifications on the group are derived. In addition,...

We show that a wide variety of non linear cellular automata can be written as a semidirect product of linear ones and that these CAs can be predicted in parallel time O log t This class includes any CA whose rule when written as an algebra is a solvable group We also show with an induction on levels of commutators that CAs based on nilpotent groups can be predicted in parallel time O log t

We describe three ways of modifying the relativistic Heisenberg algebra-first one not linked with quantum symmetries, second and third related with the formalism of quantum groups. The third way is based on the identification of generalized deformed phase space with the semidirect product of two dual Hopf algebras describing quantum group of motions and the corresponding quantum Lie algebra. As...

For an object A of a category of interest C we construct the group with operations B(A) and the semidirect product B(A) ⋉ A and prove that there exists an actor of A in C if and only if B(A) ⋉ A ∈ C. The cases of groups, Lie, Leibniz, asso-ciative, commutative associative, alternative algebras, crossed and precrossed modules are considered. The paper contains some results for the case Ω 2 = {+,...

The main contribution of this work is a new type of graph product, which we call the zig-zag product. Taking a product of a large graph with a small graph, the resulting graph inherits (roughly) its size from the large one, its degree from the small one, and its expansion properties from both! Iteration yields simple explicit constructions of constant-degree expanders of arbitrary size, startin...