arXiv subjects

Sooran Kang

Publications and source records attributed to Sooran Kang.

22 records · Page 2Linked to original sources

arXiv2013

The primitive ideals of the Cuntz-Krieger algebra of a row-finite higher-rank graph with no sources

We catalogue the primitive ideals of the Cuntz-Krieger algebra of a row-finite higher-rank graph with no sources. Each maximal tail in the vertex set has an abelian periodicity group of finite rank at most that of the graph; the primitive ideals in the Cuntz-Krieger algebra are indexed by pairs consisting of a maximal tail and a character of its periodicity group. The Cuntz-Krieger algebra is primitive if and only if the whole vertex set is a maximal tail and the graph is aperiodic.

math.OA↗

arXiv2012

Aperiodicity and the primitive ideal space of a row-finite $k$-graph $C^*$-algebra

We describe the primitive ideal space of the $C^{\ast}$-algebra of a row-finite $k$-graph with no sources when every ideal is gauge invariant. We characterize which spectral spaces can occur, and compute the primitive ideal space of two examples. In order to do this we prove some new results on aperiodicity. Our computations indicate that when every ideal is gauge invariant, the primitive ideal space only depends on the 1-skeleton of the $k$-graph in question.

math.OA↗

arXiv2011

Co-universal C*-algebras associated to aperiodic k-graphs

We construct a representation of each finitely aligned aperiodic k-graph Λ on the Hilbert space H^{ap} with basis indexed by aperiodic boundary paths in Λ. We show that the canonical expectation on B(H^{ap}) restricts to an expectation of the image of this representation onto the subalgebra spanned by the final projections of the generating partial isometries. We then show that every quotient of the Toeplitz algebra of the k-graph admits an expectation compatible with this one. Using this, we prove that the image of our representation, which is canonically isomorphic to the Cuntz-Krieger algebra, is co-universal for Toeplitz-Cuntz-Krieger families consisting of nonzero partial isometries.

math.OA↗

arXiv2009

The Yang-Mills functional and Laplace's equation on quantum Heisenberg manifolds

In this paper, we discuss the Yang-Mills functional and a certain family of its critical points on quantum Heisenberg manifolds using noncommutative geometrical methods developed by A. Connes and M. Rieffel. In our main result, we construct a certain family of connections on a projective module over a quantum Heisenberg manifold that give rise to critical points of the Yang-Mills functional. Moreover, we show that this set of solutions can be described as a set of solutions to Laplace's equation on quantum Heisenberg manifolds.

math.OA↗