Even Kakutani Equivalence via α-Equivalences and β-Equivalences

Even Kakutani Equivalence via Α and Β Equivalence In

In this paper we discuss the relationship between two of the fundamental examples of restricted orbit equivalence: even Kakutani equivalence and α equivalence. Both equivalence relations arise in the context of representations of ergodic and measure preserving Rd actions. The first is related to the Ambrose-Kakutani Theorem [1]: every free, measure preserving and ergodic R action can be represe...

Kakutani Equivalence via ~ Α and ~ Β Equivalence In

We show that an even Kakutani equivalence class of Z2 actions is “spanned” by ~ α and ~ β equivalence classes where ~ α = {1+α1, 1+ α2}, ~ β = {1 + β1, 1 + β2} and {1, α −1 i , β −1 i } are rationally independent for i = 1, 2. Namely, given such vectors ~ α and ~ β and two evenly Kakutani equivalent Z2 actions S and T , we show that U is ~ α -equivalent to S and ~ β -equivalent to T . Date: Apr...

Equivalences in Bicategories

In this paper, we establish some connections between the concept of an equivalence of categories and that of an equivalence in a bicategory. Its main result builds upon the observation that two closely related concepts, which could both play the role of an equivalence in a bicategory, turn out not to coincide. Two counterexamples are provided for that goal, and detailed proofs are given. In par...

Block Theory via Stable and Rickard Equivalences

On Monoidal Equivalences and Ann-equivalences

The equivalence between a monoidal category and a strict one has been proved by some authors such as Nguyen Duy Thuan [8], Christian Kassel [2], Peter Schauenburg [7]. In this paper, we show another proof of the problem by constructing a strict monoidal category M(C) consisting of M -functors and M morphisms of a category C and we prove C is equivalent to it. The proof is based on a basic chara...