In this paper, we define a group T_ρ(G) of p-endotrivial κG-modules and a generalized Dade group D_ρ(G) for a finite group G. We prove that T_ρ(G)≌T_ρ(H)whenever the subgroup H contains a normalizer of a Sylow p...In this paper, we define a group T_ρ(G) of p-endotrivial κG-modules and a generalized Dade group D_ρ(G) for a finite group G. We prove that T_ρ(G)≌T_ρ(H)whenever the subgroup H contains a normalizer of a Sylow p-subgroup of G, in this case, K(G)≌K(H). We also prove that the group D_ρ(G) can be embedded into T_ρ(G) as a subgroup.展开更多
Let G be a semisimple group over an algebraically closed field of characteristic p > 0. We give a(partly conjectural) closed formula for the character of many indecomposable tilting rational G-modules assuming that...Let G be a semisimple group over an algebraically closed field of characteristic p > 0. We give a(partly conjectural) closed formula for the character of many indecomposable tilting rational G-modules assuming that p is large.展开更多
We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In parti...We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In particular, we show that if an Artin algebra is switched from the other, then they have the same representation dimension.展开更多
文摘In this paper, we define a group T_ρ(G) of p-endotrivial κG-modules and a generalized Dade group D_ρ(G) for a finite group G. We prove that T_ρ(G)≌T_ρ(H)whenever the subgroup H contains a normalizer of a Sylow p-subgroup of G, in this case, K(G)≌K(H). We also prove that the group D_ρ(G) can be embedded into T_ρ(G) as a subgroup.
基金G.Lusztig was supported by National Science Foundation of USA(GrantNo.DMS-1303060)by a Simons Fellowship
文摘Let G be a semisimple group over an algebraically closed field of characteristic p > 0. We give a(partly conjectural) closed formula for the character of many indecomposable tilting rational G-modules assuming that p is large.
基金supported by the Cultivation Fund of the Key Scientific and Technical Innovation Project(707004)the Doctorate Program FOUNDATION(20040027002)Ministry of Education of China,The partial support from NSF of China is also acknowledged
文摘We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In particular, we show that if an Artin algebra is switched from the other, then they have the same representation dimension.
