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
Aqueous zinc ion batteries(AZIBs)are a promising energy storage technology due to their cost-effectiveness and safety.Organic materials with sustainable and designable structures are of great interest as AZIBs cath-od...Aqueous zinc ion batteries(AZIBs)are a promising energy storage technology due to their cost-effectiveness and safety.Organic materials with sustainable and designable structures are of great interest as AZIBs cath-odes.However,small molecules in organic cathode materials face dissolution problems and suboptimal cycle life,whereas large molecules suffer from a low theoretical capacity due to their inert carbon skeletons.Here,we designed two covalent organic framework(COF)materials(benzoquinoxaline benzoquinone-based COF(BB-COF)and triquinoxalinylene benzoquinone-based COF(TB-COF))with the same structure and number of energy storage groups to investigate the correlation between the densities of active sites and electrochemi-cal performance.We conclude that the electrochemical behavior of organic conjugate-based energy storage materials lacks a linear correlation with active site quantity.Adjusting active site densities is crucial for mate-rial advancement.BB-COF and TB-COF with dual active sites(C=O and C=N)exhibit distinct characteristics.TB-COF,which has dense active groups,shows a high initial capacity(222 mAh g^(-1)).Conversely,BB-COF,which features a large conjugated ring diameter,presents superior rate performance and enduring cycle stability.It even maintains stable cycling for 2000 cycles at-40℃.In-situ electrochemical quartz crystal mic-robalance tests reveal the energy storage mechanism of BB-COF,in which H+storage is followed by Zn2+storage.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 National Natural Science Foundation of China(Nos.22279160 and 22109134)Guangdong Basic and Applied Basic Research Foundation(2022A1515010920)+3 种基金the Outstanding Youth Basic Research Project of Shenzhen(RCYX20221008092934093)the China Postdoctoral Science Foundation(2023M733670)Special Research Assistant Funding Project of the Chinese Academy of Sciencessupported by the public computing service platform provided by SIAT.
文摘Aqueous zinc ion batteries(AZIBs)are a promising energy storage technology due to their cost-effectiveness and safety.Organic materials with sustainable and designable structures are of great interest as AZIBs cath-odes.However,small molecules in organic cathode materials face dissolution problems and suboptimal cycle life,whereas large molecules suffer from a low theoretical capacity due to their inert carbon skeletons.Here,we designed two covalent organic framework(COF)materials(benzoquinoxaline benzoquinone-based COF(BB-COF)and triquinoxalinylene benzoquinone-based COF(TB-COF))with the same structure and number of energy storage groups to investigate the correlation between the densities of active sites and electrochemi-cal performance.We conclude that the electrochemical behavior of organic conjugate-based energy storage materials lacks a linear correlation with active site quantity.Adjusting active site densities is crucial for mate-rial advancement.BB-COF and TB-COF with dual active sites(C=O and C=N)exhibit distinct characteristics.TB-COF,which has dense active groups,shows a high initial capacity(222 mAh g^(-1)).Conversely,BB-COF,which features a large conjugated ring diameter,presents superior rate performance and enduring cycle stability.It even maintains stable cycling for 2000 cycles at-40℃.In-situ electrochemical quartz crystal mic-robalance tests reveal the energy storage mechanism of BB-COF,in which H+storage is followed by Zn2+storage.
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.
