Factorisation structures of algebras and coalgebras

1998/09/11 by S. Caenepeel, Bogdan Ion, B. Ion +7
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/9809063

22 pages

openalex publication_date 1998/09/11 · arxiv created 1999/02/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the factorisation problem for bialgebras: when a bialgebra K factorises as K=HL, where H and L are algebras and coalgebras (but not necessarly bialgebras). Given two maps R: H\ot L→ L\ot H and W:L\ot H→ H\ot L, we introduce a product L_W\bowtie_R H and give necessary and sufficient conditions for L_W\bowtie_R H to be a bialgebra. It turns out that K factorises as K=HL if and only if K≅ L_W\bowtie_R H for some maps R and W. As examples of this product we recover constructions introduced by Majid and Radford. Also, some of the pointed Hopf algebras that were recently constructed bu Beattie, D\u asc\u alescu and Grünenfelder appear as special cases.

Citations

• Quantum groups and representations of monoidal categories
• Cross Product Bialgebras - Part I

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