The aim of this paper is mainly to build a new representation-theoretic realization of finite root systems through the so-called Frobenius-type triangular matrix algebras by the method of reflection functors over any ...The aim of this paper is mainly to build a new representation-theoretic realization of finite root systems through the so-called Frobenius-type triangular matrix algebras by the method of reflection functors over any field. Finally, we give an analog of APR-tilting module for this class of algebras. The major conclusions contains the known results as special cases, e.g., that for path algebras over an algebraically closed field and for path algebras with relations from symmetrizable cartan matrices. Meanwhile, it means the corresponding results for some other important classes of algebras, that is, the path algebras of quivers over Frobenius algebras and the generalized path algebras endowed by Frobenius algebras at vertices.展开更多
The rootsystem structural characteristics of annual seedlings of Pinus koraiensis, Pinus sylvestris var. mongolica, Larix olgensis and Picea koraiensis were studied with the method of excavation at the nursery of Maoe...The rootsystem structural characteristics of annual seedlings of Pinus koraiensis, Pinus sylvestris var. mongolica, Larix olgensis and Picea koraiensis were studied with the method of excavation at the nursery of Maoershan Experimental station in the Antumn of 1992. The results showed that there were large differences in some ways, such as their root quantities,distributive depth and dense layers of root systems,etc.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11271318 and 11571173)the Zhejiang Provincial Natural Science Foundation of China(Grant No.LZ13A010001)
文摘The aim of this paper is mainly to build a new representation-theoretic realization of finite root systems through the so-called Frobenius-type triangular matrix algebras by the method of reflection functors over any field. Finally, we give an analog of APR-tilting module for this class of algebras. The major conclusions contains the known results as special cases, e.g., that for path algebras over an algebraically closed field and for path algebras with relations from symmetrizable cartan matrices. Meanwhile, it means the corresponding results for some other important classes of algebras, that is, the path algebras of quivers over Frobenius algebras and the generalized path algebras endowed by Frobenius algebras at vertices.
文摘The rootsystem structural characteristics of annual seedlings of Pinus koraiensis, Pinus sylvestris var. mongolica, Larix olgensis and Picea koraiensis were studied with the method of excavation at the nursery of Maoershan Experimental station in the Antumn of 1992. The results showed that there were large differences in some ways, such as their root quantities,distributive depth and dense layers of root systems,etc.
