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december 2016 Algebra depth in tensor categories
Lars Kadison
Bull. Belg. Math. Soc. Simon Stevin 23(5): 721-752 (december 2016). DOI: 10.36045/bbms/1483671623

Abstract

Study of the quotient module of a finite-dimensional Hopf subalgebra pair in order to compute its depth yields a relative Maschke Theorem, in which semisimple extension is characterized as being separable, and is therefore an ordinary Frobenius extension. We study the core Hopf ideal of a Hopf subalgebra, noting that the length of the annihilator chain of tensor powers of the quotient module is linearly related to the depth, if the Hopf algebra is semisimple. A tensor categorical definition of depth is introduced, and a summary from this new point of view of previous results are included. It is shown in a last section that the depth, Bratteli diagram and relative cyclic homology of algebra extensions are Morita invariants.

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Lars Kadison. "Algebra depth in tensor categories." Bull. Belg. Math. Soc. Simon Stevin 23 (5) 721 - 752, december 2016. https://doi.org/10.36045/bbms/1483671623

Information

Published: december 2016
First available in Project Euclid: 6 January 2017

zbMATH: 1376.16031
MathSciNet: MR3593572
Digital Object Identifier: 10.36045/bbms/1483671623

Subjects:
Primary: 16D20, 16D90, 16T05, 18D10, 20C05

Rights: Copyright © 2016 The Belgian Mathematical Society

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Vol.23 • No. 5 • december 2016
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