The Green rings of the 2-rank Taft algebra and its two relatives twisted

2013/05/31 by Yunnan Li, Naihong Hu · 37 citations
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Cellular algebra #Combinatorics #Commutative Algebra and Its Applications #Geometry #Hopf algebra #Mathematics #Pure mathematics #Rank (graph theory) #Representation (politics) #Representation theory of Hopf algebras #Twist #Type (biology) #math.RT #msc:16G10 #msc:16G60 #msc:16N20 #msc:16S35 #msc:16T99 #msc:17B37 #msc:19A22 #msc:20G42 #msc:81R50

paper · pdf · doi:10.1016/j.jalgebra.2014.04.006

published in Journal of Algebra 410, 1-35 (Elsevier BV) · J. Algebra (to appear), 34 pages (revised the noncommutativity of Green ring of 2-rank Taft algebra \bar A, rewrote the proofs of Jacobson radicals of the three Green algebras, added some remarks and updated references, etc.)

arxiv created 2014/04/15 · openalex publication_date 2014/05/03 · arxiv updated 2014/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In the paper, the representation rings (or the Green rings) for a family of Hopf algebras of tame type, the 2-rank Taft algebra (at q=-1) and its two relatives twisted by 2-cocycles are explicitly described via a representation theoretic analysis. It turns out that the Green rings can serve to detect effectively the twist-equivalent Hopf algebras here.

Citations

• Quantum Divided Power Algebra, Q-Derivatives, and Some New Quantum Groups

Cited by

• Modular tensor categories arising from central extensions and related applications
• On 4n-dimensional neither pointed nor semisimple Hopf algebras and the associated weak Hopf algebras
• Green Rings of Pointed Rank One Hopf algebras of Non-nilpotent Type
• Indecomposable decomposition of tensor products of modules over Drinfeld Doubles of Taft algebras
• Green Rings of Finite Dimensional Pointed Rank One Hopf algebras of Nilpotent Type
• Realization of U_q(sp_2n) within the Differential Algebra on Quantum Symplectic Space
• Green rings of Drinfeld Doubles of Taft algebras

Related

• The Green rings of the generalized Taft Hopf algebras
• The Projective Class Rings of a family of pointed Hopf algebras of Rank two
• The Green Rings of Taft algebras
• Green rings of Drinfeld Doubles of Taft algebras
• Stable Green ring of the Drinfeld doubles of the generalised Taft algebras (corrections and new results)