Pure Math colloquium

Benjamin Steinberg, City College of New York

"Groupoid algebras and C*-algebras"

Groupoid C*-algebras form a unifying framework for a number of classes of C*-algebras including commutative ones, group C^*-algebras, group action cross products and Cuntz-Krieger, or graph, C*-algebras. Often purely algebraic properties of these algebras can be understood in terms of the groupoids, e.g., simplicity, Morita equivalence, the primitive ideal structure.

Over the past decade, Leavitt path algebras have become very popular objects in noncommutative algebra. They are discrete analogues, defined over any base commutative ring, of graph C*-algebras. It has been observed by many authors that there are very tight analogies between Leavitt path algebras and graph C*-algebras, but a common unifying framework was lacking.

In 2009 I introduced a purely algebraic analogue of groupoid C*-algebras. My original motivation was to study inverse semigroup algebras but in the back of my mind was to create this uniform framework. A group of operator theorists, in particular Brown, Sims and Orloff-Clark, have also begun working on groupoid algebras. There are now results describing Morita equivalence, modules, simplicity, primitivity and semiprimitivity of groupoid algebras in groupoid terms. May of the commonalities between Leavitt path algebras and graph C*-algebras have received a uniform explanation. But there are many other interesting classes of groupoid C*-algebras whose discrete analogues remain to be explored.

Please note room - MC 4060.

Refreshments will be served in MC 5158B at 3:30pm.

All are welcome!