Open Access
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


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.


Download Citation

Lars Kadison. "Algebra depth in tensor categories." Bull. Belg. Math. Soc. Simon Stevin 23 (5) 721 - 752, december 2016.


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

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

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

Keywords: core Hopf ideals , Frobenius extension , Morita equivalent ring extensions , relative Maschke theorem , semisimple extension , subgroup depth , tensor category

Rights: Copyright © 2016 The Belgian Mathematical Society

Vol.23 • No. 5 • december 2016
Back to Top