Some unitary representations of Thompson's groups F and T

2014/12/24 by Jones, Vaughan F. R. · 4 citations
#20C99 #20F65 #46L37 #57M25 #81R15 #82B20 #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Group Theory (math.GR) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1412.7740

Abstract

In a "naive" attempt to create algebraic quantum field theories on the circle, we obtain a family of unitary representations of Thompson's groups T and F for any subfactor. The Thompson group elements are the "local scale transformations" of the theory. In a simple case the coefficients of the representations are polynomial invariants of links. We show that all links arise and introduce new "oriented" subgroups \overrightarrow F

Cited by

• Finitely presented simple groups with no piecewise projective actions
• Constructing Thompson representatives via pointed links
• Soft inductive limits of operator systems and a noncommutative Lazar-Lindenstrauss theorem
• Thompson's Group V and Virtual Link Theory

Related

• Quantum fields for unitary representations of Thompson's groups F and T
• Pythagorean representations of Thompson's groups
• A Family of Projective Representations of the Thompson Group and Lifting Problems
• From skein theory to presentations for Thompson group
• Thompson's Group V and Virtual Link Theory