On the module category of Leavitt path algebras

Abstract: Leavitt path algebras were introduced in [1] as algebraic analogues of graph $C^{\*}$-algebras and as natural generalizations of Leavitt algebras of type $(1,n)$ built in [2]. Moreover, they turn out to be perfect localizations of path algebras [3]. The various ring-theoretical properties of these algebras have been actively investigated. In contrast, the investigation of their module category is still at an early stage. In this talk we focus on the structure of the simple, projective and injective modules over certain classes of Leavitt path algebras, presenting results which are part of a joint project with Gene Abrams and Alberto Tonolo.

[1] G. Abrams, G. Aranda Pino, The Leavitt path algebra of a graph, J. Algebra 293 (2005), 319 - 334.

[2] W.G. Leavitt, The module type of a ring, Trans. Amer. Math. Soc. 103 (1962), 113 - 130.

[3] P.Ara, M. Brustenga, Module theory over Leavitt path algebras and K -theory, J. Pure Appl. Algebra 214 (2010) 1131–1151

category theoryrings and algebras

Audience: researchers in the discipline

( slides )

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Additive categories between algebra and functional analysis

Series comments: Aims & Scope: Exchange ideas and foster collaboration between researchers from representation theory and functional analysis working on categorical aspects of the theory. In addition to research talks, there will be four mini-courses of introductory character.

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