Let G be a group. Two elements x, y are said to be in the same z-class if their centralizers are conjugate in G. The conjugacy classes give a partition of G. Further decomposition of the conjugacy classes into z-classes provides an important information about the internal structure of the group. Let V be a vector space of dimension n over a field F of characteristic different from 2. Let B be a...

Generalised Scherk-Schwarz reductions in which compactification on a circle is accompanied by a twist with an element of the global symmetry G typically lead to gauged supergravities and are classified by the monodromy matrices, up to conjugation by the global symmetry. For compactifications of IIB supergravity on a circle, G = SL(2, R) and there are three distinct gauged supergravities that re...

Solomon’s descent algebra is used to define a family of signed measures MW,x for a finite Coxeter group W and x > 0. The measures corresponding to W of type An arise from the theory of card shuffling. Formulas for these measures are obtained and conjectured in special cases. The eigenvalues of the associated Markov chains are computed. By elementary algebraic group theory, choosing a random sem...

In this paper we prove a combination theorem for Veech subgroups of the mapping class group analogous to the first Klein-Maskit combination theorem for Kleinian groups in which two Fuchsian subgroups are amalgamated along a parabolic subgroup. As a corollary, we construct subgroups of the mapping class group (for all genus at least 2), which are isomorphic to non-abelian closed surface groups i...

A non-elementary Möbius group generated by twoparabolics is determined up to conjugation by one complex parameter and the parameter space has been extensively studied. In this paper, we use the results of [7] to obtain an additional structure for the parameter space, which we term the two-parabolic space. This structure allows us to identify groups that contain additional conjugacy classes of p...

Generalized conjugation is the action of a group on its underlying set given by (g, x) 7→ φ(g)xg, where φ : G → G is some fixed endomorphism. Here we study combinatorial properties of the sizes of the orbits of the preceding action. In particular, we reduce the problem to a simpler case if φ has a nontrivial kernel or if it is an inner automorphism, and we give a construction that allows a part...

We define a Rohlin property for Z-actions on UHF algebras and show a non-commutative Rohlin type theorem. Among those actions with the Rohlin property, we classify product type actions up to outer conjugacy. We consider two classes of UHF algebras. For UHF algebras in one class including the CAR algebra, there is one and only one outer conjugacy class of product type actions and for UHF algebra...