Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 23, Number 5 (2016), 721-752.
Algebra depth in tensor categories
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.
Bull. Belg. Math. Soc. Simon Stevin, Volume 23, Number 5 (2016), 721-752.
First available in Project Euclid: 6 January 2017
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Primary: 16D20: Bimodules 16D90: Module categories [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality 16T05: Hopf algebras and their applications [See also 16S40, 57T05] 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23] 20C05: Group rings of finite groups and their modules [See also 16S34]
Kadison, Lars. Algebra depth in tensor categories. Bull. Belg. Math. Soc. Simon Stevin 23 (2016), no. 5, 721--752. doi:10.36045/bbms/1483671623. https://projecteuclid.org/euclid.bbms/1483671623