Hopf algebroids and H-separable extensions
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- by Lars Kadison PDF
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Abstract:
Since an H-separable extension $A | B$ is of depth two, we associate to it dual bialgebroids $S := \operatorname {End}{}_B\!A_B$ and $T := (A \otimes _B A)^B$ over the centralizer $R$ as in Kadison-Szlachányi. We show that $S$ has an antipode $\tau$ and is a Hopf algebroid. $T^{\operatorname {op}}$ is also Hopf algebroid under the condition that the centralizer $R$ is an Azumaya algebra over the center $Z$ of $A$. For depth two extension $A | B$, we show that $\operatorname {End}{}_A\!A\otimes _B\! A \cong T \ltimes \operatorname {End}{}_B\!A$.References
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Additional Information
- Lars Kadison
- Affiliation: Matematiska Institutionen, Göteborg University, S-412 96 Göteborg, Sweden
- Address at time of publication: Department of Mathematics and Statistics, University of New Hampshire, Durham, New Hamphsire 03824
- Email: kadison@math.chalmers.se, kadison@math.unh.edu
- Received by editor(s): January 11, 2002
- Received by editor(s) in revised form: April 22, 2002
- Published electronically: December 30, 2002
- Additional Notes: The author thanks Tomasz Brzezinski and U.W.S. for discussions and a hospitable visit to Swansea in the fall of 2001, as well as NORDAG in Bergen for partial support.
- Communicated by: Martin Lorenz
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2993-3002
- MSC (2000): Primary 13B02, 16H05, 16W30, 46L37, 81R15
- DOI: https://doi.org/10.1090/S0002-9939-02-06876-4
- MathSciNet review: 1993204