On Lat-Igusa-Todorov algebras.

K. Igusa and G. Todorov [Fields Inst. Commun. 45, 201–204 (2005; Zbl 1082.16011)] introduced two functions known as Igusa-Todorov functions, which led J. Wei to introduce Igusa-Todorov algebras in [Adv. Math. 222, No. 6, 2215–2226 (2009; Zbl 1213.16007)]. Wei also proved that Igusa-Todorov algebras verify the finitistic dimension conjecture. In [On certain strongly quasi-hereditary algebras. Oxford: University of Oxford (PhD Thesis) (2015)], T. Conde showed that the exterior algebras Λ(km) are not Igusa-Todorov algebras for all uncountable field k and m ≥ 3. Recently, D. Bravo et al. [J. Algebra 580, 63–83 (2021; Zbl 1476.16005)] introduced Lat-Igusa-Todorov algebras, and proved that Lat-Igusa-Todorov algebras verify the finitistic dimension conjecture as well. Moreover, selfinjective algebras are Lat-Igusa-Todorov algebras. In particular, Conde’s examples are Lat-Igusa-Todorov algebras. In the paper under review, the authors provide sufficient conditions for an algebra to be a Lat-Igusa-Todorov algebra. Next they give a construction of the algebras having only trivial 0-Igusa-Todorov subcategories. Note that an algebra having only trivial 0-Igusa-Todorov subcategories is an Igusa-Todorov algebra if and only if it is a Lat-Igusa-Todorov algebra. Finally, they provide some examples of algebras which have only trivial 0-Igusa-Todorov subcategories, are not Lat-Igusa-Todorov, and verify the finitistic dimension conjecture.