A Family of Projective Representations of the Thompson Group and Lifting Problems

2018/12/04 by Yang, Jun
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1812.01587

Abstract

The Thompson group F has a natural unitary representation on H=L²[0,1]. With some projections, we construct a family of projective unitary representations on a Fermionic Fock space associated with H. It comes from the representation of the associated CAR algebra. After H²(F;S¹) is obtained, we mainly study whether any of these projective unitary representations can be lifted to an ordinary one. We will discuss the lifting problem of these projective representations.

Related

• Some unitary representations of Thompson's groups F and T
• Pythagorean representations of Thompson's groups
• Atomic representations of R. Thompson's groups and Cuntz's algebra
• Projective representations on operator algebras
• From skein theory to presentations for Thompson group