Mixed quiver algebras

Abstract

In this paper we introduce a new class of $K$-algebras associated with quivers. Given any finite chain ${\mathbf{K}}_r:K=K_0\subseteq K_1\subseteq ...\subseteq K_r$ of fields and a chain ${\mathbf{E}}_r:H_0\subset H_1\subset ...\subset H_r=E^0$ of hereditary saturated subsets of the set of vertices $E^0$ of a quiver $E$, we build the mixed path algebra $P_{{\mathbf{K}}_r}(E,{\mathbf{H}}_r)$, the mixed Leavitt path algebra $L_{{\mathbf{K}}_r}(E,{\mathbf{H}}_r)$ and the mixed regular path algebra $Q_{{\mathbf{K}}_r}(E,{\mathbf{H}}_r)$ and we show that they share many properties with the unmixed species $P_K(E)$, $L_K(E)$ and $Q_K(E)$.

12 pages

References in corpus (1)

• Module theory over Leavitt path algebras and $K$-theory

Cited by in corpus (1)

• Module theory over Leavitt path algebras and $K$-theory