Let A be a finite dimensional k-algebra and T be a supportτ-tilting right A-module.In this note,we give lower and upper bounds for the global dimension of the endomorphism algebra End_(A)(T)under some mild conditions...Let A be a finite dimensional k-algebra and T be a supportτ-tilting right A-module.In this note,we give lower and upper bounds for the global dimension of the endomorphism algebra End_(A)(T)under some mild conditions.Finally,we give some examples to illustrate that both the upper and lower bounds can be reached.展开更多
Associated with each finite directed quiver Q is a quasi-hereditary algebra. the so-called twisted double of the path algebra kQ. Characteristic tilting modules over this class of quasi-hereditary algebras are constru...Associated with each finite directed quiver Q is a quasi-hereditary algebra. the so-called twisted double of the path algebra kQ. Characteristic tilting modules over this class of quasi-hereditary algebras are constructed. Their endonorphism algebras are explicitly described. It turns out that this class of quasi-hereditary algebras is closed under taking the Ringel dual.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 consider whether the tilting properties of a tilting A-module T and a tilting B-module T′ can convey to their tensor product T T′. The main result is that T T′ turns out to be an （n ＋ m）-tilting A B-modu...We consider whether the tilting properties of a tilting A-module T and a tilting B-module T′ can convey to their tensor product T T′. The main result is that T T′ turns out to be an （n ＋ m）-tilting A B-module, where T is an m-tilting A-module and T′ is an n-tilting B-module.展开更多
This paper gives the relationships among partial tilting objects （tilting objects） of categories of graded left A-modules of type G, left A-modules, left Ae-modules and A#-modules, and then proves that for graded pa...This paper gives the relationships among partial tilting objects （tilting objects） of categories of graded left A-modules of type G, left A-modules, left Ae-modules and A#-modules, and then proves that for graded partial tilting modules, there exist the Bongartz complements in the category of graded A-modules.展开更多
Morita equivalence was established by Morita in the late 1950's. Here most of the recent developments in this theory are reviewed and some results are presented.
The effect of ocean wave breaking as a non-Bragg mechanism on backscattering cross-section and modulation transfer functions （MTF） of radar was investigated based on Bragg resonance theory and parametric method. The...The effect of ocean wave breaking as a non-Bragg mechanism on backscattering cross-section and modulation transfer functions （MTF） of radar was investigated based on Bragg resonance theory and parametric method. The result showed that the additional effect of wave breaking on backscattering cross-section is not more than 20% except for the small incident angle of VV polarized electromagnetic （e.m.） wave but is significant for HH polarized e.m. wave. Breaking waves lead to increase in the modulus of tilt modulation MTF and the larger the wind speed, the faster the increase. For large incident angle, the modulus of tilt modulation MTF with wave breaking decreases quickly with incident angle for HH polarization and approach to that without wave breaking for VV polarization. The hydrodynamic MTF increases 30%-60% when considering wave breaking and the increase is larger for HH polarization than for VV polarization.展开更多
Gorenstein injective modules and dimensions have been studied extensively by many authors. In this paper, we investigate Gorenstein injective modules and dimensions relative to a Wakamatsu tilting module.
Abstract Let T be a Wakamatsu tilting module. A module M is called （n, T）-copure injective （resp. （n, T）-copure flat） if εT^1（N, M） = 0 （resp. Г1^T（N, M） = 0） for any module N with T-injective dimension ...Abstract Let T be a Wakamatsu tilting module. A module M is called （n, T）-copure injective （resp. （n, T）-copure flat） if εT^1（N, M） = 0 （resp. Г1^T（N, M） = 0） for any module N with T-injective dimension at most n （see Definition 2.2）. In this paper, it is shown that M is （n, T）-copure injective if and only if M is the kernel of an In（T）-precover f ： A → B with A ∈ ProdT. Also, some results on Prod T-syzygies are presented. For instance, it is shown that every nth Prod T-syzygy of every module, generated by T, is （n, T）-copure injective.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
基金supported by the National Natural Science Foundation of China(11971255,11901567,12071120)supported by the Hunan Provincial Natural Science Foundation of China(2023JJ30008)the National Natural Science Foundation of China(12371034).
文摘Let A be a finite dimensional k-algebra and T be a supportτ-tilting right A-module.In this note,we give lower and upper bounds for the global dimension of the endomorphism algebra End_(A)(T)under some mild conditions.Finally,we give some examples to illustrate that both the upper and lower bounds can be reached.
基金Supported partially by Alexander von Humboldt FoundationNational Natural Science Foundation of China (Grant No. 19971009).
文摘Associated with each finite directed quiver Q is a quasi-hereditary algebra. the so-called twisted double of the path algebra kQ. Characteristic tilting modules over this class of quasi-hereditary algebras are constructed. Their endonorphism algebras are explicitly described. It turns out that this class of quasi-hereditary algebras is closed under taking the Ringel dual.
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Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11471269, 61373140）, the Natural Science Foundation of Fujian Province （2016J01002）, and 2016 Incubation Program for Scientific Research Talent of Distinguished Young of Colledges and Universities in Fujian Province.
文摘We consider whether the tilting properties of a tilting A-module T and a tilting B-module T′ can convey to their tensor product T T′. The main result is that T T′ turns out to be an （n ＋ m）-tilting A B-module, where T is an m-tilting A-module and T′ is an n-tilting B-module.
基金the National Natural Science Foundation of China （Nos. 10371101 10671161）+2 种基金 the Natural Science Foundation of Fujian Province （Nos. Z0511022） and the Foundation of the Education Committee of Fujian Province （Nos. JA050206 JA06008 JB04215）.
文摘This paper gives the relationships among partial tilting objects （tilting objects） of categories of graded left A-modules of type G, left A-modules, left Ae-modules and A#-modules, and then proves that for graded partial tilting modules, there exist the Bongartz complements in the category of graded A-modules.
文摘Morita equivalence was established by Morita in the late 1950's. Here most of the recent developments in this theory are reviewed and some results are presented.
基金Supported by the High-Tech Research and Development Program of China (863 Program. Nos. 2001AA633070 and 2003AA604040)the National Basic Research Program of China (973 Program, No. 2005CB422307)
文摘The effect of ocean wave breaking as a non-Bragg mechanism on backscattering cross-section and modulation transfer functions （MTF） of radar was investigated based on Bragg resonance theory and parametric method. The result showed that the additional effect of wave breaking on backscattering cross-section is not more than 20% except for the small incident angle of VV polarized electromagnetic （e.m.） wave but is significant for HH polarized e.m. wave. Breaking waves lead to increase in the modulus of tilt modulation MTF and the larger the wind speed, the faster the increase. For large incident angle, the modulus of tilt modulation MTF with wave breaking decreases quickly with incident angle for HH polarization and approach to that without wave breaking for VV polarization. The hydrodynamic MTF increases 30%-60% when considering wave breaking and the increase is larger for HH polarization than for VV polarization.
基金supported by National Natural Science Foundation of China (Grant Nos. 11026141,11071111)the Zhejiang Provincial Natural Science Foundation of China (Grant Nos. D7080064,Y6100173)
文摘Gorenstein injective modules and dimensions have been studied extensively by many authors. In this paper, we investigate Gorenstein injective modules and dimensions relative to a Wakamatsu tilting module.
文摘Abstract Let T be a Wakamatsu tilting module. A module M is called （n, T）-copure injective （resp. （n, T）-copure flat） if εT^1（N, M） = 0 （resp. Г1^T（N, M） = 0） for any module N with T-injective dimension at most n （see Definition 2.2）. In this paper, it is shown that M is （n, T）-copure injective if and only if M is the kernel of an In（T）-precover f ： A → B with A ∈ ProdT. Also, some results on Prod T-syzygies are presented. For instance, it is shown that every nth Prod T-syzygy of every module, generated by T, is （n, T）-copure injective.
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.
