On the structure of irreducible Yetter-Drinfeld modules over $ D $

Yiwei Zheng; Yiwei Zheng

doi:10.3934/math.20241035

AIMS Mathematics

2024, Volume 9, Issue 8: 21321-21336. doi: 10.3934/math.20241035

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Research article

On the structure of irreducible Yetter-Drinfeld modules over $ D $

Yiwei Zheng ^,

School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China

Received: 14 May 2024 Revised: 13 June 2024 Accepted: 18 June 2024 Published: 02 July 2024
MSC : 16T05, 16T99

A class of algebras $ D(m, d, \xi) $ introduced by ^[22] were not pointed and generated by the coradical of $ D(m, d, \xi) $. Let $ D $ be the quotient of $ D(m, d, \xi) $ module the principle ideal $ (g^m-1) $. First, we describe all simple left modules of $ D $. Then, according to Radford's method, we construct the Yetter-Drinfeld module over $ D $ by the tensor product of a simple module of $ D $ and $ D $ itself. Hence, we find some simple left Yetter-Drinfeld modules over $ D $, and the relevant braidings are of a triangular type.
- Yetter-Drinfeld module,
- Hopf algebra
Citation: Yiwei Zheng. On the structure of irreducible Yetter-Drinfeld modules over $ D $[J]. AIMS Mathematics, 2024, 9(8): 21321-21336. doi: 10.3934/math.20241035

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Abstract

A class of algebras $ D(m, d, \xi) $ introduced by ^[22] were not pointed and generated by the coradical of $ D(m, d, \xi) $. Let $ D $ be the quotient of $ D(m, d, \xi) $ module the principle ideal $ (g^m-1) $. First, we describe all simple left modules of $ D $. Then, according to Radford's method, we construct the Yetter-Drinfeld module over $ D $ by the tensor product of a simple module of $ D $ and $ D $ itself. Hence, we find some simple left Yetter-Drinfeld modules over $ D $, and the relevant braidings are of a triangular type.

References

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