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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 …
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…
Williams' conjecture holds for graphs of Gelfand-Kirillov dimension three
Tran Quang Do, Roozbeh Hazrat, Tran Giang Nam
A graph of Gelfand-Kirillov dimension three is a connected finite essential graph such that its Leavitt path algebra has Gelfand-Kirillov dimension three. We provide number-theoret…
The uniform dimension of a monoid with applications to graph algebras
Luiz Gustavo Cordeiro, Daniel Gonçalves, Roozbeh Hazrat
We adapt Goldie's concept of uniform dimensions from module theory over rings to -monoids. A -monoid is said to have uniform dimension if is the largest number…
On structural connections between sandpile monoids and weighted Leavitt path algebras
Roozbeh Hazrat, Tran Giang Nam
In this article, we establish the relations between a sandpile graph, its sandpile monoid and the weighted Leavitt path algebra associated with it. Namely, we show that the lattice…