Exact Borel subalgebras of tensor algebras of quasi-hereditary algebras

Given two quasi-hereditary algebras, their tensor product is quasi-hereditary. In this article, we show that given two exact Borel subalgebras for these quasi-hereditary algebras, their tensor product is an exact Borel subalgebra. Moreover, we describe in which cases the tensor product of two regular exact Borel subalgebras is again regular. Additionally, we investigate tensor algebras of generalised species of quasi-hereditary algebras and exact Borel subalgebras thereof.