Exact Borel subalgebras of strandardly stratified algebras emulate the role of classic Borel subalgebras of complex semi-simple Lie algebras. Up to Morita equivalence, every standardly stratified algebra has an exact Borel subalgebra. By their recursive nature, standardly stratified algebras come equipped with a chain of standardly stratified quotient algebras (good quotients) and another chain of standardly stratified centraliser subalgebras (good subalgebras). In this talk, we shall see that exact Borel subalgebras are compatible, in more than one way, with good quotients and good subalgebras of standardly stratified algebras.

This is based on joint work with Julian Külshammer.