The Grothendieck ring of quantum double of quaternion group

Hua Sun; Jia Pang; Yanxi Shen

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 3, page 881-896
  • ISSN: 0011-4642

Abstract

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Let 𝕜 be an algebraically closed field of characteristic p ≠ 2 , and let Q 8 be the quaternion group. We describe the structures of all simple modules over the quantum double D ( 𝕜 Q 8 ) of group algebra 𝕜 Q 8 . Moreover, we investigate the tensor product decomposition rules of all simple D ( 𝕜 Q 8 ) -modules. Finally, we describe the Grothendieck ring G 0 ( D ( 𝕜 Q 8 ) ) by generators with relations.

How to cite

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Sun, Hua, Pang, Jia, and Shen, Yanxi. "The Grothendieck ring of quantum double of quaternion group." Czechoslovak Mathematical Journal 74.3 (2024): 881-896. <http://eudml.org/doc/299302>.

@article{Sun2024,
abstract = {Let $\mathbb \{k\}$ be an algebraically closed field of characteristic $p\ne 2$, and let $Q_8$ be the quaternion group. We describe the structures of all simple modules over the quantum double $D(\mathbb \{k\}Q_8)$ of group algebra $\mathbb \{k\}Q_8$. Moreover, we investigate the tensor product decomposition rules of all simple $D(\mathbb \{k\}Q_8)$-modules. Finally, we describe the Grothendieck ring $G_0(D(\mathbb \{k\}Q_8))$ by generators with relations.},
author = {Sun, Hua, Pang, Jia, Shen, Yanxi},
journal = {Czechoslovak Mathematical Journal},
keywords = {Grothendieck ring; simple module; quantum double; quaternion group},
language = {eng},
number = {3},
pages = {881-896},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Grothendieck ring of quantum double of quaternion group},
url = {http://eudml.org/doc/299302},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Sun, Hua
AU - Pang, Jia
AU - Shen, Yanxi
TI - The Grothendieck ring of quantum double of quaternion group
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 3
SP - 881
EP - 896
AB - Let $\mathbb {k}$ be an algebraically closed field of characteristic $p\ne 2$, and let $Q_8$ be the quaternion group. We describe the structures of all simple modules over the quantum double $D(\mathbb {k}Q_8)$ of group algebra $\mathbb {k}Q_8$. Moreover, we investigate the tensor product decomposition rules of all simple $D(\mathbb {k}Q_8)$-modules. Finally, we describe the Grothendieck ring $G_0(D(\mathbb {k}Q_8))$ by generators with relations.
LA - eng
KW - Grothendieck ring; simple module; quantum double; quaternion group
UR - http://eudml.org/doc/299302
ER -

References

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