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 chara...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.展开更多
Let K〈X〉 = K（X1,..., Xn） be the free K-algebra on X = {X1,..., Xn} over a field K, which is equipped with a weight N-gradation （i.e., each Xi is assigned a positive degree）, and let G be a finite homogeneous GrS...Let K〈X〉 = K（X1,..., Xn） be the free K-algebra on X = {X1,..., Xn} over a field K, which is equipped with a weight N-gradation （i.e., each Xi is assigned a positive degree）, and let G be a finite homogeneous GrSbner basis for the ideal I = （G） of K（X） with respect to some monomial ordering 〈 on K（X）. It is shown that if the monomial algebra K（X）/（LM（6）） is semiprime, where LM（6） is the set of leading monomials of 6 with respect to 〈, then the N-graded algebra A ： K（X）/I is semiprimitive in the sense of Jacobson. In the case that G is a finite nonhomogeneous Gr6bner basis with respect to a graded monomial ordering 〈gr, and the N-filtration FA of the algebra A = K（X）/I induced by the N-grading filtration FK（X） of K（X） is considered, if the monomial algebra K（X）/（LM（6）） is semiprime, then it is shown that the associated N-graded algebra G（A） and the Rees algebra A of A determined by FA are all semiprimitive.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11301144,11771122,11801141).
文摘We give a complete description of the Batalin-Vilkovisky algebra structure on Hochschild cohomology of the self-injective quadratic monomial algebras.
基金National Natural Science Foundation of China(Grant No.10601036)
文摘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Project supported by the National Natural Science Foundation of China （10971044）.
文摘Let K〈X〉 = K（X1,..., Xn） be the free K-algebra on X = {X1,..., Xn} over a field K, which is equipped with a weight N-gradation （i.e., each Xi is assigned a positive degree）, and let G be a finite homogeneous GrSbner basis for the ideal I = （G） of K（X） with respect to some monomial ordering 〈 on K（X）. It is shown that if the monomial algebra K（X）/（LM（6）） is semiprime, where LM（6） is the set of leading monomials of 6 with respect to 〈, then the N-graded algebra A ： K（X）/I is semiprimitive in the sense of Jacobson. In the case that G is a finite nonhomogeneous Gr6bner basis with respect to a graded monomial ordering 〈gr, and the N-filtration FA of the algebra A = K（X）/I induced by the N-grading filtration FK（X） of K（X） is considered, if the monomial algebra K（X）/（LM（6）） is semiprime, then it is shown that the associated N-graded algebra G（A） and the Rees algebra A of A determined by FA are all semiprimitive.
