ScholarLens Back to search
2013•International Journal of MathematicsRequires access

II1 FACTORS AND EQUIVALENCE RELATIONS WITH DISTINCT FUNDAMENTAL GROUPS

Jan Keersmaekers, An Speelman

Open publisher page 3 citations

Abstract

We construct a group measure space II1 factor that has two nonconjugate Cartan subalgebras. We show that the fundamental group of the II1 factor is trivial, while the fundamental group of the equivalence relation associated with the second Cartan subalgebra is nontrivial. This is not absurd as the second Cartan inclusion is twisted by a 2-cocycle.

About this research paper

What this paper is about

We construct a group measure space II1 factor that has two nonconjugate Cartan subalgebras. We show that the fundamental group of the II1 factor is trivial, while the fundamental group of the equivalence relation associated with the second Cartan subalgebra is nontrivial. This is not absurd as the second Cartan inclusion is twisted by a 2-cocycle.

Why it matters

OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

We construct a group measure space II1 factor that has two nonconjugate Cartan subalgebras. We show that the fundamental group of the II1 factor is trivial, while the fundamental group of the equivalence relation associated with the second Cartan subalgebra is nontrivial. This is not absurd as the second Cartan inclusion is twisted by a 2-cocycle.

Key concepts: Mathematics, Cartan subalgebra, Equivalence (formal languages), Pure mathematics, Equivalence relation, Fundamental group, Quotient algebra, Factor (programming language)

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
II1 FACTORS AND EQUIVALENCE RELATIONS WITH DISTINCT FUNDAMENTAL GROUPS — Research Paper | ScholarLens