2008/05/15 by Margaret Beattie, Beattie, Margaret, Miodrag C. Iovanov +3
Mathematics · Physics and Astronomy · #16W30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.0805.2401
openalex publication_date 2008/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For A a Hopf algebra of arbitrary dimension over a field K, it is well-known that if A has nonzero integrals, or, in other words, if the coalgebra A is co-Frobenius, then the space of integrals is one-dimensional and the antipode of A is bijective. Bulacu and Caenepeel recently showed that if H is a dual quasi-Hopf algebra with nonzero integrals, then the space of integrals is one-dimensional, and the antipode is injective. In this short note we show that the antipode is bijective.