In 2021 the authors D. Bravo, M. Lanzilotta, O. Mendoza and J. Vivero gave a generalization of the concept of Igusa-Todorov algebra and proved that those algebras, named Lat-Igusa-Todorov (LIT for short), satisfy the finitistic dimension conjecture. In this paper we explore the scope of that generalization and give conditions for a triangular matrix algebra to be LIT in terms of the algebras and the bimodule used in its definition. As an application we obtain that the tensor product of an LIT \(\mathbb {K}\)-algebra with a path algebra of a quiver whose underlying graph is a tree, is LIT.

中文翻译：

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三角lat-igusa-todorov代数

2021 年，作者 D. Bravo、M. Lanzilotta、O. Mendoza 和 J. Vivero 对 Igusa-Todorov 代数的概念进行了概括，并证明了这些代数，名为 Lat-Igusa-Todorov（简称 LIT），满足有限维数猜想。在本文中，我们探讨了该泛化的范围，并根据代数和在其定义中使用的双模给出了三角矩阵代数为 LIT 的条件。作为一个应用程序，我们得到 LIT \(\mathbb {K}\) -代数与基础图是树的箭袋的路径代数的张量积是 LIT。