The dilogarithmic central extension of the Ptolemy-Thompson group via the Kashaev quantization
- 주제(키워드) Quantum Teichmuller theory , Thompson group T , Ptolemy-Thompson group , Kashaev quantization , Braided Ptolemy-Thompson group , Universal Teichmuller space , Stable braid group , Infinite braid group
- 주제(기타) Mathematics
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 ACADEMIC PRESS INC ELSEVIER SCIENCE
- 발행년도 2016
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000162018
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.aim.2016.02.016
초록/요약
Quantization of universal Teichmuller space provides projective representations of the Ptolemy-Thompson group, which is isomorphic to the Thompson group T. This yields certain central extensions of T by Z, called dilogarithmic central extensions. We compute a presentation of the dilogarithmic central extension (T) over cap (Kash) of T resulting from the Kashaev quantization, and show that it corresponds to 6 times the Euler class in H-2 (T; Z). Meanwhile, the braided Ptolemy-Thompson groups T*, T-# of Funar-Kapoudjian are extensions of T by the infinite braid group B-infinity and by abelianizing the kernel B-infinity one constructs central extensions T-ab*, T-ab(#) of T by Z, which are of topological nature. We show (T) over cap (Kash) congruent to T-ab(#) Our result is analogous to that of Funar and Sergiescu, who computed a presentation of another dilogarithmic central extension (T) over cap (CF) of T resulting from the Chekhov-Fock (-Goncharov) quantization and thus showed that it corresponds to 12 times the Euler class and that (T) over cap (CF) congruent to T-ab*. In addition, we suggest a natural relationship between the two quantizations in the level of projective representations. (C) 2016 Elsevier Inc. All rights reserved.
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