摘要
Let A be a monomial quasi-hereditary algebra with a pure strong exact Borel subalgebra B.It is proved that the category of induced good modules over B is contained in the category of good modules over A;that the characteristic module of A is an induced module of that of B via the exact functor-(?)_B A if and only if the induced A-module of an injective B-module remains injective as a B-module.Moreover,it is shown that an exact Borel subalgebra of a basic quasi-hereditary serial algebra is right serial and that the characteristic module of a basic quasi-hereditary serial algebra is exactly the induced module of that of its exact Borel subalgebra.
Let A be a monomial quasi-hereditary algebra with a pure strong exact Borel subalgebra B. It is proved that the category of induced good modules over B is contained in the category of good modules over A; that the characteristic module of A is an induced module of that of B via the exact functor — ? B A if and only if the induced A-module of an injective B-module remains injective as a B-module. Moreover, it is shown that an exact Borel subalgebra of a basic quasi-hereditary serial algebra is right serial and that the characteristic module of a basic quasi-hereditary serial algebra is exactly the induced module of that of its exact Borel subalgebra.
基金
National Natural Science Foundation of China(Grant No.10601036)
