On the type of a category of complexes of fixed size and the strong global dimension

CHAIO, CLAUDIA, GONZALEZ CHAIO ALFREDO, PRATTI ISABEL.

Algebras and Representation Theory

SPRINGER

Lugar: Berlin; Año: 2019 vol. 22 p. 1343 - 1370

1386-923X

We prove that if the strong global dimension $eta$ of an algebra $A,$%is finite, then $mathbf{C_{eta +1}}({m proj}, A)$ is of finite type if and only if for each $n geq 2$, $mathbf{C_n}({m proj}, A)$ is of finite type. Moreover, we also prove some implications in order to know if for some positive integer is $mathbf{C_{n}}({m proj}, A)$ of infinite type.We determine the strong global dimension of some piecewise hereditary finite dimensional algebras taking into account their ordinary quivers with relations.