Seminar on partial actions and Fell bundles

This is a Masters/PhD seminar I'm offering in the summer semester 2021 at WWU Münster. It takes place on Wednesdays at 14:15 via Zoom. Please email me if you would like to have a link to our meetings.

Tentative schedule:

  • April 14 (Laurin Schwering). Partial actions on topological spaces: basic definitions, examples, restriction and globalization. (Chapter 5 of [2].) Notes.

  • April 21 (Laurin Schwering). Partial actions on C*-algebras and their crossed products: basic definitions, construction of the full crossed product, covariant representations. (Chapters 11 and 13 of [2], may need to read parts of Chapter 6 as well.) Notes.

  • April 28 (Rafaela Gesing). Fell bundles: basic definitions, construction of the associated C*-algebras, saturation, connections to partial actions. (Chapter 16 of [2].) Notes.

  • May 5 (Holger Spellmann). Reduced cross-sectional algebras of Fell-bundles: representations on Hilbert modules, regular representations of Fell bundles, Fourier coefficients, reduced crossed product of a partial action. (Chapter 17 of [2], also parts of Chapter 15 – but only the necessary material.) Notes.

  • May 12 (Julian Kranz). Fell's absorption principle and graded C*-algebras: Fell's absorption for Fell bundles, consequences for Fell bundles and partial actions, (topological) gradings on C*-algebras. (Chapters 18 and 19 of [2].) Notes.

  • May 19 (Julian Kranz). Amenability for Fell bundles: definition, approximation property, applications to partial actions. (Chapter 20 of [2].) Notes.

  • May 26. No seminar.

  • June 2. No seminar.

  • June 9 (Holger Spellmann). Duality for Fell bundles: (restricted) smash products, dual (partial) actions. (Chapter 26 in [2].) Morita equivalence for partial actions (Part of Chapter 15 in [2]). Notes.

  • June 16 (Zahra Hasanpour). Globalization of partial actions on C*-algebras: uniqueness, the commutative case, Morita-globalizations, Morita equivalence of the crossed products. (Chapter 28 in [2].) Time permitting: characterization of globalizable partial actions ([3]). Notes.

  • June 23 (Siegfried Echterhoff). K-theory for semigroup C*-algebras and partial crossed products ([5]).

  • June 30 (Marzieh Forough). Morita equivalence for Fell bundles ([4]).

  • Bibliography:

    • [1] R. Exel. Circle actions on C*-algebras, partial automorphisms, and a generalized Pimsner- Voiculescu exact sequence, J. Funct. Anal., 122 (1994), 361--401.
    • [2] R. Exel. Partial dynamical systems, Fell bundles and applications, Mathematical Surveys and Monographs, American Mathematical Society (2017), volume 224.
    • [3] D. Ferraro. Construction of globalizations for partial actions on rings, algebras, C*-algebras and Hilbert bimodules. Rocky Mountain J. Math. 48 (2018), 181--217.
    • [4] D. Ferraro and F. Abadie. Equivalence of Fell bundles over groups. J. Operator Theory 81 (2019), no. 2, 273--319.
    • [5] X. Li, K-theory for semigroup C*-algebras and partial crossed products. Preprint arXiv:2003.03858 (2020).