Integrals for (dual) quasi-Hopf algebras. Applications

29Citations
Citations of this article
6Readers
Mendeley users who have this article in their library.

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. © 2003 Published by Elsevier Inc.

Cite

CITATION STYLE

APA

Bulacu, D., & Caenepeel, S. (2003). Integrals for (dual) quasi-Hopf algebras. Applications. Journal of Algebra, 266(2), 552–583. https://doi.org/10.1016/S0021-8693(03)00175-3

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free