Let n be a natural number, and let A be an indecomposable cellular algebra such that the spectrum of its Cartan matrix C is of theform {n, 1,..., 1}. In general, not every natural number could be the number of non-iso...Let n be a natural number, and let A be an indecomposable cellular algebra such that the spectrum of its Cartan matrix C is of theform {n, 1,..., 1}. In general, not every natural number could be the number of non-isomorphic simple modules over such a cellular algebra. Thus, two natural questions arise: (1) which numbers could be the number of non-isomorphic simple modules over such a cellular algebra A ? (2) Given such a number, is there a cellular algebra such that its Cartan matrix has the desired property ? In this paper, we shall completely answer the first question, and give a partial answer to the second question by constructing cellular algebras with the pre-described Cartan matrix.展开更多
Let F be an algebracially closed field of characteristic p】2, and L be the p<sup>n</sup>-dimensional Zassenhaus algebra with the maximal invariant subalgebra L<sub>0</sub> and the standard fil...Let F be an algebracially closed field of characteristic p】2, and L be the p<sup>n</sup>-dimensional Zassenhaus algebra with the maximal invariant subalgebra L<sub>0</sub> and the standard filtration {L<sub>i</sub>}|<sub>i=-1</sub><sup>p<sup>n</sup>-2</sup>. Then the number of isomorphism classes of simple L-modules is equal to that of simple L<sub>0</sub>-modules, corresponding to an arbitrary character of L except when its height is biggest. As to the number corresponding to the exception there was an earlier result saying that it is not bigger than p<sup>n</sup>.展开更多
基金This research work was supported by CFKSTIP(Grant No.704004)the Doctor Program Foundation(Grant No.20040027002),Ministry of Education of Chinapartially by National Natural Science Foundation of China(Grant No.103331030).
文摘Let n be a natural number, and let A be an indecomposable cellular algebra such that the spectrum of its Cartan matrix C is of theform {n, 1,..., 1}. In general, not every natural number could be the number of non-isomorphic simple modules over such a cellular algebra. Thus, two natural questions arise: (1) which numbers could be the number of non-isomorphic simple modules over such a cellular algebra A ? (2) Given such a number, is there a cellular algebra such that its Cartan matrix has the desired property ? In this paper, we shall completely answer the first question, and give a partial answer to the second question by constructing cellular algebras with the pre-described Cartan matrix.
基金Supported in part by the National Natural Science Foundation of China Grant 19801022the Scientifictechnological Major Project of Educational Ministry of China, Grant 99036.
文摘Let F be an algebracially closed field of characteristic p】2, and L be the p<sup>n</sup>-dimensional Zassenhaus algebra with the maximal invariant subalgebra L<sub>0</sub> and the standard filtration {L<sub>i</sub>}|<sub>i=-1</sub><sup>p<sup>n</sup>-2</sup>. Then the number of isomorphism classes of simple L-modules is equal to that of simple L<sub>0</sub>-modules, corresponding to an arbitrary character of L except when its height is biggest. As to the number corresponding to the exception there was an earlier result saying that it is not bigger than p<sup>n</sup>.
