Quantum Spheres and Projective Spaces as Graph Algebras

By J. Hong, W. Szymański. 2002

160 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d2f066ed20a0de68db10a809af92b1f0610d72ad

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Aidan Sims
2. Iain Raeburn
3. M. Tomforde
4. J. Hong
5. W. Szymański
6. Trent Yeend
7. Samuel B. G. Webster
8. P. Muhly

In Geometry and Topology

1. Aidan Sims
2. Iain Raeburn
3. J. Hong
4. W. Szymański
5. S. P. Smith
6. Samuel B. G. Webster
7. R. Hazlewood
8. P. Muhly

In Mathematical Physics

1. Aidan Sims
2. M. Tomforde
3. Iain Raeburn
4. J. Hong
5. W. Szymański
6. Trent Yeend
7. Samuel B. G. Webster
8. P. Muhly

Citations in the corpus

• CATEGORY EQUIVALENCES INVOLVING GRADED MODULES OVER PATH ALGEBRAS OF QUIVERS (2011, background): “It also follows from the main result in [21], which was written after this paper, that QGr(k〈x, y〉/(y2)) is equivalent to QGr(kQ).”
• Quantum lens spaces and graph algebras (2003, background): “We assume that E is a row-finite graph (i.e., each vertex of E emits only finitely many edges) without sinks, since this is all we need in the present article.”
• Remarks on some fundamental results about higher-rank graphs and their C*-algebras (2011, background): “C∗-algebras associated to graphs and k-graphs have attracted significant attention recently because they at once encompass a great many interesting examples [2, 6, 11, 17], and are remarkably tractable [3, 4, 5, 7, 12, 13, 21].”
• Product systems of graphs and the Toeplitz algebras of higher-rank graphs | NOVA. The University of Newcastle's Digital Repository (2003, methodology): “This theorem is apparently beyond the reach of Fowler’s theory, and our proof requires a detailed analysis of the expectation onto the diagonal in T C∗(E).”
• The primitive ideal space of the $C^{*}$-algebras of infinite graphs (2002, background): “Also, graph algebras appearing in the context of some compact quantum manifolds [ 11 , 12] are not simple, and it is important to know their ideal structure.”
• Regularity and dimension spectrum of the equivariant spectral triple for the odd dimensional quantum spheres (2008, unknown): “Then πl : zk 7→ Yk,q gives a faithful representation of C(S2l+1 q ) on Hl (see lemma 4.1 and remark 4.5, [ 10 ]).”
• Topological Quivers (2003, background): “For other C∗-algebras, including some that arise in representation theory (see [37, 38, 42]) and the theory of quantum spaces (see [23, 24]), it is an issue of considerable importance in their analysis to determine how they may be represented by a graph.”