We review topologically Nistor’s computation of the homogeneous part of the periodic cyclic cohomology of crossed products Γ⋉A of torsion-free discrete groups Γ with a complex Γ-algebra A. We use periodic cyclic cohomology associated to bornological algebras. Let G be a complex connected semisimple Lie group and B be a minimal parabolic subgroup of G. Applied to torsion-free discrete subgroups ...

We define and compute higher rank analogs of PandharipandeThomas stable pair invariants in primitive classes for K3 surfaces. Higher rank stable pair invariants for Calabi-Yau threefolds have been defined by Sheshmani [She11b, She11a] using moduli of pairs of the form On → F for F purely one-dimensional and computed via wall-crossing techniques. These invariants may be thought of as virtually c...

For any n×n matrix A , we use the joint higher rank numerical range, Λk(A, . . . ,Am) , to define the higher rank numerical hull of A . We characterize the higher rank numerical hulls of Hermitian matrices. Also, the higher rank numerical hulls of unitary matrices are studied. Mathematics subject classification (2010): 15A60,81P68.

For a higher-rank graph Λ with sources we detail a construction that creates a row-finite higher-rank graph Λ that does not have sources and contains Λ as a subgraph. Furthermore, when Λ is row-finite the Cuntz-Krieger algebra of Λ, C(Λ) is a full corner of C(Λ), the Cuntz-Krieger algebra of Λ.