Journal article
The Antipode of a Dual Quasi-Hopf Algebra with Nonzero Integrals is Bijective
Algebras and Representation Theory, Vol.12(2), pp.251-255
10/2009
DOI: 10.1007/s10468-009-9148-3
Abstract
For a Hopf algebra A 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.
Details
- Title: Subtitle
- The Antipode of a Dual Quasi-Hopf Algebra with Nonzero Integrals is Bijective
- Creators
- M Beattie - Department of Mathematics and Computer Science Mount Allison University Sackville New Brunswick Canada E4L 1E6M Iovanov - Fac. Matematica & Informatica University of Bucharest Str. Academiei nr. 14 Bucharest 010014 RomaniaŞ Raianu - Mathematics Department California State University Dominguez Hills, 1000 E Victoria St Carson CA 90747 USA
- Resource Type
- Journal article
- Publication Details
- Algebras and Representation Theory, Vol.12(2), pp.251-255
- DOI
- 10.1007/s10468-009-9148-3
- ISSN
- 1386-923X
- eISSN
- 1572-9079
- Publisher
- Springer Netherlands; Dordrecht
- Language
- English
- Date published
- 10/2009
- Academic Unit
- Mathematics
- Record Identifier
- 9983985984402771
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