This paper arose out of an attempt to generalize the ’q; q−1“-basis for the centre of an Iwahori–Hecke algebra Hq found by Jones to ’q; q−1“ and to other types. Considering the Iwahori–Hecke algebra H over a subring ’ξ“ of ’q1/2; q−1/2“, where ξ = q1/2 − q−1/2, we use a new and natural definition of positivity on H to describe the “minimal” ’ξ“-basis for ZH‘ in terms of a partial order on the ...

A one-sided (resp. two-sided) shift of finite type of dimension one can be described as the set of infinite (resp. bi-infinite) sequences of consecutive edges in a finite-state automaton. While the conjugacy of shifts of finite type is decidable for one-sided shifts of finite type of dimension one, the result is unknown in the two-sided case. In this paper, we study the shifts of finite type de...

A one-sided (resp. two-sided) shift of finite type of dimension one can be described as the set of infinite (resp. bi-infinite) sequences of consecutive edges in a finite-state automaton. While the conjugacy of shifts of finite type is decidable for one-sided shifts of finite type of dimension one, the result is unknown in the two-sided case. In this paper, we study the shifts of finite type de...

The simplest nonsingular flows on closed orientable 3-manifolds are studied. We establish that each class of topological equivalence the flow a lens consists an infinite set conjugacy classes. obtain necessary and sufficient conditions for under consideration.

‎Let G be a finite group and Z(G) be the center of G‎. ‎For a subset A of G‎, ‎we define kG(A)‎, ‎the number of conjugacy classes of G that intersect A non-trivially‎. ‎In this paper‎, ‎we verify the structure of all finite groups G which satisfy the property kG(G-Z(G))=5, and classify them‎.

We prove the freeness conjecture of Broué, Malle and Rouquier for the Hecke algebras associated to most of the primitive complex 2-reflection groups with a single conjugacy class of reflections.

3 Main Results 8 3.1 Mixed-Integer Linear Programming Framework . . . . . . . . . . . . . . . . . . . . . 9 3.2 Initialization of Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Implementing Dynamical Equivalence and Linear Conjugacy . . . . . . . . . . . . . 10 3.4 Implementing Deficiency Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.5 ...

The aim of this paper is to show that L2(2 f ) are the only nonsolvable groups in which every irreducible character of even degree vanishes on just one conjugacy class. MSC 2000: 20C15

In this paper we show that all Garside groups are strongly translation discrete, that is, the translation numbers of non-torsion elements are strictly positive and for any real number r there are only finitely many conjugacy classes of elements whose translation numbers are less than or equal to r. It is a consequence of the inequality “infs(g) 6 infs(g n) n < infs(g) + 1” for a positive intege...

We prove that the conjugacy problem in a large and natural class of subgroups of right-angled Artin groups (RAAGs), can be solved in linear-time. This class of subgroups has been previously studied by Crisp and Wiest, and independently by Haglund and Wise, as fundamental groups of compact special cube complexes.