2024/03/01 by Hügel, Lidia Angeleri, Laking, Rosanna, Sentieri, Francesco · 1 citation
#16E35 #16G10 #16G20 #18E40 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2403.00475
We establish a bijection between torsion pairs in the category of finite-dimensional modules over a finite-dimensional algebra A and pairs (Z, I) formed by a closed rigid set Z in the Ziegler spectrum of A and a set I of indecomposable injective A-modules. This can be regarded as an extension of a result from τ-tilting theory which parametrises the functorially finite torsion pairs over A. We also obtain a one-one-correspondence between finite-dimensional bricks and certain (possibly infinite-dimensional) indecomposable modules satisfying a rigidity condition. Our results also hold when A is an artinian ring.