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.
- April 14 (Laurin Schwering). Partial actions on topological spaces: basic definitions, examples, restriction and globalization. (Chapter 5 of .)
- 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 , may need to read parts of Chapter 6 as well.)
- April 28 (Rafaela Gesing). Fell bundles: basic definitions, construction of the associated C*-algebras,
saturation, connections to partial actions. (Chapter 16 of .)
- 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 , 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 .) Notes.
- May 19 (Julian Kranz). Amenability for Fell bundles: definition, approximation property, applications to partial actions. (Chapter 20 of .)
- 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 .) Morita equivalence for partial actions (Part of Chapter
15 in ). 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 .) Time permitting: characterization of globalizable partial actions (). Notes.
- June 23 (Siegfried Echterhoff). K-theory for semigroup C*-algebras and partial crossed products ().
- June 30 (Marzieh Forough). Morita equivalence for Fell bundles ().
-  R. Exel. Circle actions on C*-algebras, partial automorphisms, and a generalized Pimsner-
Voiculescu exact sequence, J. Funct. Anal., 122 (1994), 361--401.
-  R. Exel. Partial dynamical systems, Fell bundles and applications, Mathematical Surveys
and Monographs, American Mathematical Society (2017), volume 224.
-  D. Ferraro. Construction of globalizations for partial actions on rings, algebras, C*-algebras
and Hilbert bimodules. Rocky Mountain J. Math. 48 (2018), 181--217.
-  D. Ferraro and F. Abadie. Equivalence of Fell bundles over groups. J. Operator Theory 81 (2019), no. 2, 273--319.
-  X. Li, K-theory for semigroup C*-algebras and partial crossed products. Preprint