2019/02/10 by Amini, Massoud, Shirinkalam, Ahmad
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary 55N91 #Secondary 46L05
paper · doi:10.48550/arxiv.1902.03593
This is a survey of a variety of equivariant (co)homology theories for operator algebras. We briefly discuss a background on equivariant theories, such as equivariant K-theory and equivariant cyclic homology. As the main focus, we discuss a notion of equivariant L2 -cohomology and equivariant L2 -Betti numbers for subalgebras of a von Neumann algebra. For graded C^*-algebras (with grading over a group) we elaborate on a notion of graded L2 -cohomology and its relation to equivariant L2-cohomology.