On 4n-dimensional neither pointed nor semisimple Hopf algebras and the associated weak Hopf algebras

2018/09/03 by Chen, Jialei, Shilin Yang, Yang, Shilin +4
Mathematics · #16D70 #16G10 #16T99 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1809.00514

openalex publication_date 2018/09/03 · openalex created_date 2018/09/27 · openalex updated_date 2026/07/28

Abstract

For a class of neither pointed nor semisimple Hopf algebras H_4n of dimension 4n, it is shown that they are quasi-triangular, which universal R-matrices are described. The corresponding weak Hopf algebras \mathfrakwH_4n and their representations are constructed. Finally, their duality and their Green rings are established by generators and relations explicitly. It turns out that the Green rings of the associated weak Hopf algebras are not commutative even if the Green rings of H_4n are commutative.

Citations

• The Green rings of the 2-rank Taft algebra and its two relatives twisted
• Finite-dimensional Hopf algebras over the smallest non-pointed basic Hopf algebra

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