Related papers: Lagrangian mechanics on centered semi-direct produ…

We show that the semidirect product of a group $C$ by $A*_D B$ is isomorphic to the free product of $A\rtimes C$ and $B\rtimes C$ amalgamated at $D\rtimes C$, where $A$, $B$ and $C$ are arbitrary groups. Moreover, we apply this theorem to…

When S is a discrete subsemigroup of a discrete group G such that G = S^{-1} S, it is possible to extend circle-valued multipliers from S to G; to dilate (projective) isometric representations of S to (projective) unitary representations of…

We extend a recent result that for the (additive) semigroup of positive integers $\mathbb{N}$, there are continuum many subdirect products of $\mathbb{N} \times \mathbb{N}$ up to isomorphism. We prove that for $U,V$ each one of $\mathbb{Z}$…

We construct the crossed product of a C(X)-algebra by an endomorphism, in such a way that the endomorphism itself becomes induced by the bimodule of continuous sections of a vector bundle. Some motivating examples for such a construction…

For a compact Lie group G, we use G-equivariant Poincar\'e duality for ordinary RO(G)-graded homology to define an equivariant intersection product, the dual of the equivariant cup product. Using this, we give a homological construction of…

Extending Goursat's Lemma we investigate the structure of subdirect products of 3-factor direct products. We give several example constructions and then provide a structure theorem showing that every such group is essentially obtained by a…

We study conditions under which subdirect products of various types of algebraic structures are finitely generated or finitely presented. In the case of two factors, we prove general results for arbitrary congruence permutable varieties,…

Consider a Lie subalgebra $\mathfrak{l} \subset \mathfrak{g}$ and an $\mathfrak{l}$-invariant open submanifold $V \subset \mathfrak{l}^{\ast}$. We demonstrate that any smooth dynamical twist on $V$, valued in $U(\mathfrak{g}) \otimes…

In this article we define the twisted product of groups as the generalization of the semidirect product of groups. We will find the necessary and sufficient condition in order that the twisted product of groups to be a group. In particular,…

We investigate Moufang loops which can be written as the semidirect product of a loop and a group. We also examine a particular class of loop extensions which arise as a result of a finite cyclic group acting as a group of semiautomorphisms…

Given an action of a groupoid by isomorphisms on a Fell bundle (over another groupoid), we form a semidirect-product Fell bundle, and prove that its $C^{*}$-algebra is isomorphic to a crossed product.

We ascertain conditions and structures on categories and semigroups which admit the construction of pseudo-products and trace products respectively, making their connection as precise as possible. This topic is modelled on the ESN Theorem…

In a recent paper, the author defined an operation of tensor product for a large class of $2$-representations of $\mathcal{U}^{+}$, the positive half of the $2$-category associated to $\mathfrak{sl}_{2}$. In this paper, we prove that the…

Let \G be a (weak) quasi-Hopf algebra. Using a two-sided \G-coaction on an algebra \M, we construct what we call the diagonal crossed product as a new associative algebra structure on \M\otimes \dG, where \dG is the dual of \G. This…

Let M be a Galois cover of a nilpotent coadjoint orbit of a complex semisimple Lie group. We define the notion of a PERFECT Dixmier algebra for M and show how this produces a graded (non-local) equivariant star product on M with several…

For each group G which decomposes into a finitary direct product of free groups of finite rank we construct a regular band B such that the free idempotent generated semigroup over B contains a maximal subgroup isomorphic to G. In…

Let V be a finite dimensional complex superspace and G a simple (or a ``close'' to simple) Lie superalgebra of matrix type, i.e., a Lie subsuperalgebra in GL(V). Under the classical invariant theory for G we mean the description of…

The recently developed theory of partial actions of discrete groups on $C^*$-algebras is extended. A related concept of actions of inverse semigroups on $C^*$-algebras is defined, including covariant representations and crossed products.…

Formal actions of Lie algebras over vector spaces are introduced in a purely algebraic way, as a mimic of infinitesimal operations of Banach Lie algebras over Banach analytic manifolds. In analogy with the case of abstract groups, complete…

Let $\E$ be a finite dimensional Hilbert space. This note finds all factorizations of the right shift semigroup $\S^\E=(S_t^\E)_{t\ge 0}$ on $L^2(\R_+,\E)$ into the product of $n$ commuting contractive semigroups, i.e., characterizes all…