Integrals for (dual) quasi-Hopf algebras. Applications

By Daniel Bulacu, Stefaan Caenepeel. 2001

47 citations recorded by the source corpus.

Abstract A classical result in the theory of Hopf algebras concerns the uniqueness and existence of integrals: for an arbitrary Hopf algebra, the integral space has dimension ⩽1, and for a finite-dimensional Hopf algebra, this dimension is exactly one. We generalize these results to quasi-Hopf algebras and dual quasi-Hopf algebras. In particular, it will follow that the bijectivity of the antipode follows from the other axioms of a finite-dimensional quasi-Hopf algebra. We give a new version of the Fundamental Theorem for quasi-Hopf algebras. We show that a dual quasi-Hopf algebra is co-Frobenius if and only if it has a non-zero integral. In this case, the space of left or right integrals has dimension one.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c8b555e965a118a616a077e5132943aeca221964

Citations in the corpus

• On the Frobenius–Schur indicators for quasi-Hopf algebras (2003, unknown): “If H is finite-dimensional then S is always a bijection by a result of Bulacu and Caenepeel [ 1 ].”