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2018•arXiv (Cornell University)Open access

A Projective Representations of the Thompson Group F and Its Lifting Problem

Jun Yang

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Abstract

The Thompson group $F$ has a canonical unitary representation on $H=L^2[0,1]$. With a special projection, we construct a projective unitary representation on a Fermionic Fock space associated with $H$. This comes from the representation of the CAR algebra of $H$. Then, by computing the 2nd cohomology group, we will be able to decide if this projective unitary representation can be lifted to an ordinary representation. We will mainly discuss the lifting problem of this projective representation.

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What this paper is about

The Thompson group $F$ has a canonical unitary representation on $H=L^2[0,1]$. With a special projection, we construct a projective unitary representation on a Fermionic Fock space associated with $H$. This comes from the representation of the CAR algebra of $H$. Then, by computing the 2nd cohomology group, we will be able to decide if this projective unitary representation can be lifted to an ordinary representation. We will mainly discuss the lifting problem of this projective representation.

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Available abstract

The Thompson group $F$ has a canonical unitary representation on $H=L^2[0,1]$. With a special projection, we construct a projective unitary representation on a Fermionic Fock space associated with $H$. This comes from the representation of the CAR algebra of $H$. Then, by computing the 2nd cohomology group, we will be able to decide if this projective unitary representation can be lifted to an ordinary representation. We will mainly discuss the lifting problem of this projective representation.

Key concepts: Projective unitary group, Projective representation, Projective test, Mathematics, Projective space, Unitary group, Unitary state, Representation (politics)

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