11,887 research outputs found
Group actions on Smale space C*-algebras
Group actions on a Smale space and the actions induced on the C*-algebras
associated to such a dynamical system are studied. We show that an effective
action of a discrete group on a mixing Smale space produces a strongly outer
action on the homoclinic algebra. We then show that for irreducible Smale
spaces, the property of finite Rokhlin dimension passes from the induced action
on the homoclinic algbera to the induced actions on the stable and unstable
C*-algebras. In each of these cases, we discuss the preservation of
properties---such as finite nuclear dimension, Z-stability, and classification
by Elliott invariants---in the resulting crossed products.Comment: 30 pages. Final version, to appear in Ergodic Theory Dynam. System
Pfaffian quartic surfaces and representations of Clifford algebras
Given a nondegenerate ternary form of degree 4 over an
algebraically closed field of characteristic zero, we use the geometry of K3
surfaces and van den Bergh's correspondence between representations of the
generalized Clifford algebra associated to and Ulrich bundles on the
surface to construct a
positive-dimensional family of irreducible representations of
The main part of our construction, which is of independent interest, uses
recent work of Aprodu-Farkas on Green's Conjecture together with a result of
Basili on complete intersection curves in to produce simple
Ulrich bundles of rank 2 on a smooth quartic surface
with determinant This implies that every smooth quartic
surface in is the zerolocus of a linear Pfaffian, strengthening
a result of Beauville-Schreyer on general quartic surfaces.Comment: This paper contains a proof of the main result claimed in the
erroneous preprint arXiv:1103.0529. We also extend this result to all smooth
quartic surface
- β¦