Leavitt Path Algebras of Finite Gelfand–kirillov Dimension

“…(Note that, in view of Theorem 3.2, this can be deduced from work in [8,9].) Examples are constructed showing that this statement is no longer true if E is an infinite graph.…”

Section: Leavitt Path Algebras With Gk Dimension ≤mentioning

confidence: 98%

Leavitt path algebras satisfying a polynomial identity

2016

View full text Add to dashboard Cite

Abstract. Leavitt path algebras L of an arbitrary graph E over a field K satisfying a polynomial identity are completely characterized both in graphtheoretic and algebraic terms. When E is a finite graph, L satisfying a polynomial identity is shown to be equivalent to the Gelfand-Kirillov dimension of L being at most one, though this is no longer true for infinite graphs. It is shown that, for an arbitrary graph E, the Leavitt path algebra L has Gelfand-Kirillov dimension zero if and only if E has no cycles. Likewise, L has Gelfand-Kirillov dimension one if and only if E contains at least one cycle, but no cycle in E has an exit.

show abstract

“…We mention that [9,Theorem 6.1] extends [17,Theorem 7.2]; compare [7,Theorem 3.8]. The construction of the injective Leavitt complex is inspired by the basis of the Leavitt path algebra given by [1,Theorem 1].…”

mentioning

confidence: 99%

“…For the proof of (1) in Theorem I, we construct an explicit filtration of subcomplexes of the injective Leavitt complex I…”

mentioning

confidence: 99%

The Injective Leavitt Complex

2017

Algebr Represent Theor

View full text Add to dashboard Cite

Abstract. For a finite quiver Q without sinks, we consider the corresponding finite dimensional algebra A with radical square zero. We construct an explicit compact generator for the homotopy category of acyclic complexes of injective A-modules. We call such a generator the injective Leavitt complex of Q. This terminology is justified by the following result: the differential graded endomorphism algebra of the injective Leavitt complex of Q is quasiisomorphic to the Leavitt path algebra of Q. Here, the Leavitt path algebra is naturally Z-graded and viewed as a differential graded algebra with trivial differential.

show abstract

Leavitt Path Algebras of Finite Gelfand–kirillov Dimension

Abstract: Groebner–Shirshov Basis and Gelfand–Kirillov dimension of the Leavitt path algebra are derived.

Cited by 58 publications

References 3 publications

Completions of Leavitt path algebras

Completions of Leavitt path algebras

Leavitt path algebras satisfying a polynomial identity

The Injective Leavitt Complex

Contact Info

Product

Resources

About