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Sehnem Lab
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The lab studies the ideal structure of C*-algebras arising from group actions.
AboutAbout the lab
Constructing operator algebras from group actions
The Sehnem Lab studies functional analysis, especially operator algebra theory.
The lab is interested in various generalizations of actions of groups and semigroups on C*-algebras (such as correspondences and partial automorphisms), and works on constructing operator algebras, mainly C*-algebras, from such actions.
Non-self-adjoint operator algebras and von Neumann algebras have also played important roles in this research.
Key terms
- Operator algebra
- An algebraic structure formed by collecting linear transformations (operators) that act on an infinite-dimensional space (a Hilbert space).
- C*-algebra
- A type of operator algebra equipped with, in addition to addition and multiplication, an operation of taking adjoints and a notion of size (a norm).
- Ideal
- A part of a ring that never leaves itself when multiplied by any element of the ring. It gives a way to analyze the structure of a ring by decomposing it.
ResearchResearch themes
The lab studies functional analysis, especially operator algebra theory. It works on constructing operator algebras from generalizations of group and semigroup actions on C*-algebras, and has recently focused mainly on the ideal structure of C*-algebras arising from (partial) group actions on noncommutative C*-algebras.
*Illustrative imageGroup actions on noncommutative C*-algebras and ideal structure
The lab studies the ideal structure of C*-algebras arising from (partial) group actions on noncommutative C*-algebras, that is, from (partial) C*-dynamical systems.
*Illustrative imagePrimality and the ideal intersection property of reduced crossed products
In joint research, the lab completely characterized the primality of the reduced crossed product C*-algebra associated with an arbitrary action of a discrete group, in terms of the original C*-dynamical system.
*Illustrative imageBoundary theory for partial actions
In joint research, the lab developed a boundary theory for arbitrary partial actions of discrete groups on noncommutative C*-algebras.
MembersFaculty
- Associate ProfessorCamila Sehnem
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Hyperbolic tiling 7 7-2” Double sharp (talk), based on this picture by Jim McNeill, but with the remaining overlapping heptagons left as outlines instead of deleted. A green background to the tiling has also been added. Created using Tyler and Paint. / Public domain (cropped)
- Group actions on noncommutative C*-algebras and ideal structure: “Siegel quadratic 3,2,1000,1... ,IIM” Adam majewski / CC BY-SA 3.0 (cropped)
- Primality and the ideal intersection property of reduced crossed products: “Square symmetry – R3” Jacob Rus / CC BY-SA 4.0 (cropped)
- Boundary theory for partial actions: “Schottky (Kleinian) group limit set in plane” Adam majewski / CC BY-SA 4.0 (cropped)
- Related lab (応用数理研究部門
（小澤 登高） ): “Cayley graph of Alternating Group A5” Kathryn Cramer / CC BY-SA 4.0 (cropped) - Related lab (応用数理研究部門
（磯野 優介） ): “Bernoullishift” Andreas Mandl / CC BY-SA 3.0 (cropped) - Related lab (応用数理研究部門
（岸本 展） ): “Rogue waves breaking behavior at different crossing angles, McAllister 2019” McAllister et al 2019 / CC BY 4.0 (cropped) - Related lab (応用数理研究部門
（河村 彰星） ): “Turing Machine” Porao / Public domain (cropped)
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