Representations of the modular group arising from Drinfeld doubles of finite abelian groups

Naidu Deepak

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Representations of the modular group arising from Drinfeld doubles of finite abelian groups

机译：来自DRINFELD的模块组的表示是有限的abelian群体

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摘要

We show that the image of the representation of the modular group SL(2, Z) arising from the representation category Rep(D(G)) of the Drinfeld double D(G) of a finite abelian group G of exponent n is isomorphic to the special linear group SL(2, Z/nZ), where Z/nZ denotes the ring of integers modulo n. As a consequence, we establish that the kernel of the representation in question is the principal congruence subgroup of level n.

机译：我们证明，由指数为n的有限阿贝尔群G的德林菲尔德双D（G）的表示范畴Rep（D（G））产生的模群SL（2，Z）的表示的图像同构于特殊的线性群SL（2，Z/nZ），其中Z/nZ表示模n的整数环，我们证明了所讨论的表示的核心是n级的主同余子群。

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《Journal of algebra and its applications》 |2021年第2期|共16页
作者
Naidu Deepak;
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作者单位

Northern Illinois Univ Dept Math Sci De Kalb IL 60115 USA;

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正文语种 eng
中图分类代数、数论、组合理论;
关键词
Drinfeld double; modular tensor category; modular group; congruence subgroup;

机译：DRINFELD DOUBLE;模块化张量类别;模块化群体;一致亚组;

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1. Canonical Differential Calculi for Finitely Generated Abelian Groups and Their Fermionic Representations [J] . DAI Jian, SONG Xing-Chang, XIONG Chuan-Sheng 理论物理通讯（英文版） . 2002,第004期
2. On Unit Groups in Modular Group Algebras of Abelian Groups with Totally Projective Components [J] . Peter V.Danchev 代数集刊（英文版） . 2007,第003期
3. Duality Theorem and Drinfeld Double in Braided Tensor Categories [J] . Shouchuan Zhang 代数集刊（英文版） . 2003,第002期
4. Mapping class group representations from Drinfeld doubles of finite groups [J] . Journal of knot theory and its ramifications . 2020,第5期

机译：从DRINFELD的映射类组表示有限群体的加倍
5. Kernels of representations of Drinfeld doubles of finite groups : Open Mathematics [J] . Sebastian Burciu Open Mathematics . 2013,第11期

机译：有限群Drinfeld双打的表示核：开放数学
6. Kernels of representations of Drinfeld doubles of finite groups [J] . Sebastian Burciu Central European Journal of Mathematics . 2013,第11期

机译：Drinfeld有限组双打的表示核
7. Remarks on Applicability of Spectral Representations on Finite Non-Abelian Groups in the Design for Regularity [C] . Stankovic Radomir S., Astola Jaakko T., Moraga Claudio 40th IEEE International Symposium on Multiple-Valued Logic . 2010

机译：关于正则性设计中有限非阿贝尔群的谱表示的适用性的说明
8. Three contributions to topology, algebraic geometry and representation theory: Homological finiteness of abelian covers, algebraic elliptic cohomology theory and monodromy theorems in the elliptic setting. [D] . Yang, Yaping. 2014

机译：对拓扑，代数几何和表示理论的三个贡献：阿贝尔封面的同调有限性，代数椭圆同调理论和椭圆环境中的一峰定理。
9. Continuous family of finite-dimensional representations of a solvable Lie algebra arising from singularities [O] . Stephen S.-T. Yau 1983

机译：可奇李代数的有限维表示形式的连续族
10. MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS [O] . Deepak NAİDU 2020

机译：来自DRINFELD Dihedral群体的模块化组图像
11. Projective Representations of Finite Abelian Groups [R] . Saeed-ul-Islam, M. 1983

机译：有限阿贝尔群的投射表示

Representations of the modular group arising from Drinfeld doubles of finite abelian groups

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