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Frobenius Extensions and Weak Hopf Algebras

✍ Scribed by Lars Kadison; Dmitri Nikshych

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
211 KB
Volume
244
Category
Article
ISSN
0021-8693

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✦ Synopsis

We study a symmetric Markov extension of k-algebras N → M, a certain kind of Frobenius extension with conditional expectation that is tracial on the centralizer and dual bases with a separability property. We place a depth two condition on this extension, which is essentially the requirement that the Jones tower N → M → M 1 → M 2 can be obtained by taking relative tensor products with centralizers A = C M 1 N and B = C M 2 M . Under this condition, we prove that N → M is the invariant subalgebra pair of a weak Hopf algebra action by A, i.e., that N = M A . The endomorphism algebra M 1 = End N M is shown to be isomorphic to the smash product algebra M#A. We also extend results of W.

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