Delooping levels

In (Adv. Math. 394, 108052, 2022) V. Gélinas introduced a homological invariant, called delooping level (dell), that bounds the finitistic dimension. In this article, we introduce another homological invariant (Dell) related to the delooping level for an Artin algebra. We compare this new tool with other dimensions as the finitistic dimension or the ϕ-dimension (where ϕ is the first Igusa-Todorov function), and we also generalize Theorem 4.3. from Gélinas (Proc. Amer. Math. Soc. 149(12), 5001-5012, 2021) to truncated path algebras (Theorem 4.18). Finally, we show that for a monomial algebra A the difference dell (A) −Findim(A) can be arbitrarily large (Example 4.22).