The representation ring of a non-pointed bialgebra

Huaqing Gong; Shilin Yang; Huaqing Gong; Shilin Yang

doi:10.3934/math.2025234

AIMS Mathematics

2025, Volume 10, Issue 3: 5110-5123. doi: 10.3934/math.2025234

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The representation ring of a non-pointed bialgebra

Huaqing Gong ,
Shilin Yang ^,

School of Mathematical, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China

Received: 18 November 2024 Revised: 22 February 2025 Accepted: 28 February 2025 Published: 06 March 2025
MSC : 16D70, 16G60, 16G70, 16T05

The aim of this paper is to characterize the representation ring of a non-pointed and noncocommutative bialgebra. First, the isomorphism classes of its indecomposable modules are classified. Then the tensor product of modules is established. Finally, its representation ring is described.
- bialgebra,
- bound quiver,
- representation ring
Citation: Huaqing Gong, Shilin Yang. The representation ring of a non-pointed bialgebra[J]. AIMS Mathematics, 2025, 10(3): 5110-5123. doi: 10.3934/math.2025234

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Abstract

The aim of this paper is to characterize the representation ring of a non-pointed and noncocommutative bialgebra. First, the isomorphism classes of its indecomposable modules are classified. Then the tensor product of modules is established. Finally, its representation ring is described.

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