Infinite index subalgebras of depth two

Author:
Lars Kadison

Journal:
Proc. Amer. Math. Soc. **136** (2008), 1523-1532

MSC (2000):
Primary 16W30; Secondary 46L37, 81R50

Published electronically:
January 17, 2008

MathSciNet review:
2373579

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Abstract | References | Similar Articles | Additional Information

Abstract: An algebra extension is right depth two in this paper if its tensor-square is --isomorphic to a direct summand of any (not necessarily finite) direct sum of with itself. For example, normal subgroups of infinite groups, infinitely generated Hopf-Galois extensions and infinite-dimensional algebras are depth two in this extended sense. The added generality loses some duality results obtained in the finite theory (Kadison and Szlachányi, 2003) but extends the main theorem of depth two theory, as for example in (Kadison and Nikshych, 2001). That is, a right depth two extension has right bialgebroid over its centralizer . The main theorem: An extension is right depth two and right balanced if and only if is -Galois with respect to left projective, right -bialgebroid .

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Additional Information

**Lars Kadison**

Affiliation:
Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104-6395

Email:
lkadison@math.upenn.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-08-09077-1

Received by editor(s):
December 1, 2006

Published electronically:
January 17, 2008

Communicated by:
Martin Lorenz

Article copyright:
© Copyright 2008
American Mathematical Society