Abstract The Zassenhaus formula finds many applications in theoretical physics or mathematics, from fluid dynamics to differential geometry. non-commutativity of the elements algebra implies that exponential a sum operators cannot be expressed as product exponentials operators. can then decomposed multiplied by supplementary term which takes generally form an infinite exponentials. Such procedu...

The orthogonal group of a quadratic space over a field has been the focus of intensive research over the past fifty years. As this article will indicate, it continues to be a source of interesting problems. Zassenhaus [17] constructed a decomposition for any element in the orthogonal group of a non-degenerate quadratic space over a field of characteristic not 2. This paper will develop the fund...

The Baker-Campbell-Hausdorff (BCH) series and the Zassenhaus product are of fundamental importance for the theory of Lie groups and their applications in physics. In this paper, various methods for the computation of the terms in these expansions are compared, and a new efficient approach for the calculation of the Zassenhaus terms is introduced. Mathematica implementations for the most efficie...

Let U(KλG) be the group of units of an infinite twisted group algebra KλG over a field K. We describe the maximal FC-subgroup of U(KλG) and give a characterization of U(KλG) with finitely conjugacy classes. In the case of group algebras we obtain the Cliff-Sehgal-Zassenhaus’ theorem.

The goal of this paper is to study the action groups on Zassenhaus and lower central filtrations finitely generated pro-p groups. We shall focus semisimple case. Particular attention given presented cohomological dimension less than or equal two.

In the following, we describe a way of factoring polynomials in Fq[X] with Drinfeld modules. We furthermore analyse the complexity of the algorithm and compare it to the well-known Cantor-Zassenhaus algorithm. 1. Defining Fq[X ]-module structures with Drinfeld modules Throughout this paper we will denote A = Fq[X ], where q is a power of some prime p, and N ∈ A for the polynomial which is to be...