We started our research with the intent on answering the following question: can we find a way to calculate all the subgroups of the symmetric group. This is easier said that done, as the number of subgroups for a symmetric group grows quickly with each successive symmetric group. This problem can actually be simplified to finding the subgroup conjugacy classes. So now we have the slightly diff...

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...

We prove that the fundamental group of any Seifert 3-manifold is conjugacy separable. That is, conjugates may be distinguished in finite quotients or, equivalently, conjugacy classes are closed in the pro-finite topology.

The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper we present a new definition of conjugacy, which can be applied to an arbitrary semigroup, including semigroups with zero. We characterize this conjugacy in various semigro...

Let G be a connected reductive algebraic group over an algebraic closed field. We define a (surjective) map from the set of conjugacy classes in the Weyl group to the set of unipotent classes in G.

Let G be a simple complex classical group and g its Lie algebra. Let U~(g) be the Drinfeld-Jimbo quantization of the universal enveloping algebra U(g). We construct an explicit U~(g)-equivariant quantization of conjugacy classes of G with Levi subgroups as the stabilizers.

We construct a generator system of the annihilator of the generalized Verma module of gl(n,C) induced from any character of any parabolic subalgebra as an analogue of minors and elementary divisors. The generator system has a quantization parameter ε and it generates the defining ideal of the conjugacy class of square matrices at the classical limit ε = 0.

Let G be a group. Two elements x, y are said to be z-equivalent if their centralizers are conjugate in G. The class equation of G is the partition of G into conjugacy classes. Further decomposition of conjugacy classes into z-classes provides an important information about the internal structure of the group, cf. [8] for the elaboration of this theme. Let I(Hn) denote the group of isometries of...

Abstract We characterize conjugacy classes of isometries odd prime order in unimodular ${\mathbb {Z}}$-lattices. This is applied to give a complete classification non-symplectic automorphisms the known deformation types irreducible holomorphic symplectic manifolds up and birational conjugacy.

We define a Rohlin property for actions of Z on UHF algebras and show a noncommutative Rohlin type theorem. Among those actions with the Rohlin property, we classify product type actions up to outer conjugacy. In particular we present two classes of UHF algebras. For UHF algebras in one class, which includes the CAR algebra, there is one and only one outer conjugacy class of product type action...