1997
DOI: 10.1023/a:1004237304068
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Cited by 9 publications
(5 citation statements)
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“…where φ(x) = ln(e x + 1), (2) and all other variables are left unchanged. These transformations generate a groupoid, the Ptolemy groupoid [11], that may be abstractly characterized by generators and relations: One has a generator ω ij whenever the triangles labeled by i and j have an edge in common.…”
Section: 3mentioning
confidence: 99%
See 3 more Smart Citations
“…where φ(x) = ln(e x + 1), (2) and all other variables are left unchanged. These transformations generate a groupoid, the Ptolemy groupoid [11], that may be abstractly characterized by generators and relations: One has a generator ω ij whenever the triangles labeled by i and j have an edge in common.…”
Section: 3mentioning
confidence: 99%
“…represents the quantum deformation of the classical expression given in (2). The formulae (6) define a representation of the Ptolemy groupoid by automorphisms of A(Σ) [10].…”
Section: Representation Of the Mapping Class Group Onmentioning
confidence: 99%
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“…This interpretation should provide the basis for a deeper understanding of two-dimensional quantum gravity 3 as well as a future theory of three-dimensional quantum gravity (see e.g. 4,5 and references therein).…”
Section: Introductionmentioning
confidence: 96%