Tensor Categories and Hopf Algebras.

Cover -- Title page -- Contents -- Preface -- On finite GK-dimensional Nichols algebras of diagonal type -- 1. Introduction -- 2. Preliminaries -- 3. General results -- 4. Rank 2 -- References -- On nonassociative graded-simple algebras over the field of real numbers -- 1. Introduction -- 2. Background on gradings -- 3. Loop construction -- 4. Alternative algebras -- 5. Jordan algebras of degree 2 -- Acknowledgments -- References -- Nonsemisimple Hopf algebras of dimension 8 with the Chevalley property -- 1. Introduction -- 2. Preliminaries -- 3. Nonsemisimple Hopf algebras of dimension 8 -- 4. Nonsemisimple Hopf algebras of dimension 24 -- References -- Pointed braided tensor categories -- 1. Introduction -- 2. Preliminaries -- 3. Quantum linear spaces of symmetric type -- 4. Classification of co-quasitriangular structures on pointed Hopf algebras (Proof of Theorem 1.1) -- 5. The symmetric center of \C(Γ, ₀, , ₁) -- 6. Ribbon structures on \C(Γ, ₀, , ₁) -- 7. Metric data (Proof of Theorem 1.2) -- 8. The Drinfeld center of a pointed braided tensor category -- Acknowledgments. -- References -- Eigenvalues of the squared antipode in finite dimensional weak Hopf algebras -- 1. Introduction -- 2. Pivotal structures matched to a module category -- 3. Eigenvalues of ² -- 4. Eigenvalues of ² for dynamical quantum groups at roots of 1 -- 5. Acknowledgements. -- Appendix A. Module traces and inner-product structures -- References -- Cohen-Macaulay invariant subalgebras of Hopf dense Galois extensions -- 0. Introduction -- 1. Hom-sets of the quotient category -- 2. Hom-sets of the quotient categories of smash products -- 3. Invariant subalgebras of Hopf dense Galois extensions -- 4. Cohen-Macaulay property of as an ^{ }-module -- 5. Finite group actions on noetherian complete semilocal algebras -- References.

Bialgebra coverings and transfer of structure -- Introduction -- 1. Measurings -- 2. Partial Coverings and Transfer of Structure -- 3. Cocommutative and Graded Coverings -- 4. A Nichols Theorem for Hopf coverings -- Acknowledgements -- References -- Classifying braidings on fusion categories -- 1. Introduction -- 2. Preliminaries -- 3. Subcategories transversal to a Lagrangian algebra -- 4. Braidings on non-degenerate fusion categories -- 5. Braidings on group-theoretical categories -- Acknowledgements -- References -- Remarks on global dimensions of fusion categories -- 1. Introduction -- 2. Preliminaries -- 3. Pseudo-unitary inequality without pseudo-unitarity -- 4. Bounds for formal codegrees -- 5. Fusion categories of the same global dimension -- Appendix A. -- Acknowledgements -- References -- On Hopf algebras with triangular decomposition -- 1. Introduction -- 2. A general framework -- 3. Preliminaries on Hopf algebras -- 4. A method to construct Hopf algebras with triangular decomposition -- 5. On the representation theory of \kuu_{( , )}( ) -- Acknowedgments -- References -- Back Cover.

This volume contains the proceedings of the scientific session "Hopf Algebras and Tensor Categories", held from July 27-28, 2017, at the Mathematical Congress of the Americas in Montreal, Canada. Papers highlight the latest advances and research directions in the theory of tensor categories and Hopf algebras. Primary topics include classification and structure theory of tensor categories and Hopf algebras, Gelfand-Kirillov dimension theory for Nichols algebras, module categories and weak Hopf algebras, Hopf Galois extensions, graded simple algebras, and bialgebra coverings.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.