Steinberg Algebras

Anna Cichocka

supervisor: Michał Ziembowski

Steinberg algebras are an example of associative algebras defined based on ample topological Hausdorff groupoid. For any considered commutative ring `R` with a unit and an ample groupoid `G`, the elements of Steinberg algebra `A_R (G)` are functions acting on `G` in `R` satisfying certain specified properties. The class of Steinberg algebras `A_R (G)` is a generalization of such classes of algebras as, for example, the graph algebras of Leavitt paths.

Bibliography:

• B. Steinberg (2010), A groupoid approach to discrete inverse semigroup algebras, Advances in Mathematics 223, 2, 689–727.
• J. Renault (1980), A Groupoid Approach to C*-Algebras, vol. 793 of Lecture Notes in Mathematics. Springer-Verlag.
• L. O. Clark, C. Farthing, A. Sims, M. Tomforde (2014), A groupoid generalisation of Leavitt path algebras, Semigroup Forum 89, 3, 501–517.
• S. W. Rigby (2018), The groupoid approach to Leavitt path algebras, arXiv e-prints.