12 papers
A Minimum-Cardinality Genuinely Unextendible Product Basis in Three Qutrits
Fei Shi, Ge Bai, Xiande Zhang +2
It has remained an open question whether a genuinely unextendible product basis (GUPB) exists. We resolve this problem by constructing an explicit three-qutrit GUPB of cardinality…
Higher-Dimensional Symbolic Dynamics: A Textile Framework For 3-graphs
Roozbeh Hazrat, Promit Mukherjee, Sujit Kumar Sardar
Textile systems are best known to model two-dimensional shifts of finite type. In this article, we associate a discrete algebra with a textile system and provide a groupoid model f…
Graded Lawson-Stone Duality
Roozbeh Hazrat, Zachary Mesyan
The classical Stone duality associates to each Boolean algebra a topological space consisting of ultrafilters. Lawson's generalisation constructs a dual equivalence of categories o…
The graded Grothendieck group is full for weighted Leavitt path algebras
Remarl Joseph Damalerio, Roozbeh Hazrat, Tran Giang Nam
The Graded Classification Conjecture asserts that the graded Grothendieck group is a complete invariant for the classes of Leavitt path algebras and graph …
Higher-rank graphs and the graded -theory of Kumjian-Pask algebras
Roozbeh Hazrat, Promit Mukherjee, David Pask +1
This paper lays out the foundations of graded -theory for Leavitt algebras associated with higher-rank graphs, also known as Kumjian-Pask algebras, establishing it as a potentia…
Embedding -algebras into Leavitt algebra
Boris Bilich, Roozbeh Hazrat, Tran Giang Nam
Since the commutative monoid is a weak terminal object in the category of conical monoids with order units, there is a unital homomorphism from every Bergman…