MenuEvents for 07/30/2014 from all calendars
Workshop in Analysis and Probability Seminar
Time: 11:00AM - 12:00PM
Location: Blocker 163
Speaker: Scott Lalonde, Dartmouth College
Title: Equivalence and Exact Groupoids
Abstract: An interesting equivalence relation for locally compact Hausdorff groupoids arises when two groupoids admit suitably nice actions on the same space. This notion of groupoid equivalence is strictly weaker than isomorphism, but it is strong enough to preserve certain desirable properties. These ideas are strongly paralleled by those surrounding the theory of Morita equivalence for C*-algebras. Indeed, equivalence of groupoids is intimately connected to the Morita equivalence of the associated groupoid C*-algebras. Given this connection, I will describe how the proof of a purely C*-algebraic result can be mimicked to show that a property called exactness is preserved under groupoid equivalence. Along the way, I will discuss groupoid crossed product C*-algebras and some classical ideas that motivate the study of groupoid equivalence.
Workshop in Analysis and Probability Seminar
Time: 4:00PM - 5:00PM
Location: Blocker 163
Speaker: Robert Pluta, Sam Houston State University
Title: Noncommutative retracts
Abstract: A subalgebra S of an algebra A is called a corner of A if there is an S-bimodule M contained in A such that A = S + M (direct sum of S-bimodules). Of course the prime example is the Peirce corner S = eAe associated with an idempotent e in A, but the above definition is more general and makes no reference to idempotents. In the first part of this presentation we will give a number of basic results about corners of general algebras and C*-algebras, partly surveying [1]. In the second part we will be concerned with closed and self-adjoint corners of C*-algebras that are complemented by ideals - a notion which we consider as a noncommutative analog of topological retracts. [1] R. Pluta, Ranges of Bimodule Projections and Conditional Expectations, Cambridge Scholars Publishing, 2013.
