Mapping class group representations from Drinfeld doubles of finite groups

被引:0
|
作者
Fjelstad, Jens [1 ,2 ]
Fuchs, Jurgen [3 ]
机构
[1] Uppsala Univ, Dept Math, Box 480, S-75106 Uppsala, Sweden
[2] Orebro Univ, Dept Math, Fak Gatan 1, S-70182 Orebro, Sweden
[3] Karlstads Univ, Teoret Fys, Univ Gatan 21, S-65188 Karlstad, Sweden
基金
瑞典研究理事会;
关键词
Quantum representation; mapping class group; Drinfeld double; TORELLI GROUP; QUANTUM; RING;
D O I
10.1142/S0218216520500339
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of such representations in terms of finite group data. This allows us to establish various properties of these representations. In particular, we show that they have finite images, and that for surfaces of genus at least 3 their restriction to the Torelli group is non-trivial if and only if G is non-abelian.
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页数:61
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