The concept of Koszul differential graded (DG for short) algebra is introduced in [8].Let A be a Koszul DG algebra.If the Ext-algebra of A is finite-dimensional,i.e.,the trivial module A k is a compact object in the d...The concept of Koszul differential graded (DG for short) algebra is introduced in [8].Let A be a Koszul DG algebra.If the Ext-algebra of A is finite-dimensional,i.e.,the trivial module A k is a compact object in the derived category of DG A-modules,then it is shown in [8] that A has many nice properties.However,if the Ext-algebra is infinitedimensional,little is known about A.As shown in [15] (see also Proposition 2.2),A k is not compact if H(A) is finite-dimensional.In this paper,it is proved that the Koszul duality theorem also holds when H(A) is finite-dimensional by using Foxby duality.A DG version of the BGG correspondence is deduced from the Koszul duality theorem.展开更多
The aim of this paper is to categorify the n-th tensor power of the vector representation of U（ ο（7,C））. The main tools are certain singular blocks and projective functors of the BGG category of the complex Lie a...The aim of this paper is to categorify the n-th tensor power of the vector representation of U（ ο（7,C））. The main tools are certain singular blocks and projective functors of the BGG category of the complex Lie algebra gln.展开更多
In this paper we give a categorification of the n-th tensor products of the spin modules of enveloping algebra of lie algebra of type D4 via some subcategories and projective functors of the BGG category of the genera...In this paper we give a categorification of the n-th tensor products of the spin modules of enveloping algebra of lie algebra of type D4 via some subcategories and projective functors of the BGG category of the general linear Lie algebra gln over the complex field C.展开更多
本文围绕内蕴有限元,探讨其在数值偏微分方程中的应用,及其与离散微分几何和拓扑数据分析的潜在联系.由保持连续问题的数学与物理结构的数值离散驱动,本文简要回顾有限元外微分(Finite Element Exterior Calculus,FEEC)的发展.通过经典d...本文围绕内蕴有限元,探讨其在数值偏微分方程中的应用,及其与离散微分几何和拓扑数据分析的潜在联系.由保持连续问题的数学与物理结构的数值离散驱动,本文简要回顾有限元外微分(Finite Element Exterior Calculus,FEEC)的发展.通过经典de Rham复形及BGG复形的规范离散,提出一个扩展的形式值微分形式有限元周期表,涵盖Whitney形式、分布有限元、Regge有限元及Hessian和divdiv复形等,为张量问题的数值求解提供统一工具.本文进一步分析内蕴有限元在Riemann-Cartan几何、广义连续介质及引力波计算等跨学科应用中的潜力.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 10801099,10731070)the Doctoral Program Foundation of the Ministry of Education of China (No. 20060246003)
文摘The concept of Koszul differential graded (DG for short) algebra is introduced in [8].Let A be a Koszul DG algebra.If the Ext-algebra of A is finite-dimensional,i.e.,the trivial module A k is a compact object in the derived category of DG A-modules,then it is shown in [8] that A has many nice properties.However,if the Ext-algebra is infinitedimensional,little is known about A.As shown in [15] (see also Proposition 2.2),A k is not compact if H(A) is finite-dimensional.In this paper,it is proved that the Koszul duality theorem also holds when H(A) is finite-dimensional by using Foxby duality.A DG version of the BGG correspondence is deduced from the Koszul duality theorem.
基金Supported by the Natural Science Foundation of Beijing(Grant No.1122006)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.201111103110011)Science and Technology Foundation of BJUT(Grant No.ykj-4787)
文摘The aim of this paper is to categorify the n-th tensor power of the vector representation of U（ ο（7,C））. The main tools are certain singular blocks and projective functors of the BGG category of the complex Lie algebra gln.
基金Supported by National Natural Science Foundation of China(Grant No.11271043)Natural Science Foundation of Beijing(Grant No.1122006)Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.201111103110011)
文摘In this paper we give a categorification of the n-th tensor products of the spin modules of enveloping algebra of lie algebra of type D4 via some subcategories and projective functors of the BGG category of the general linear Lie algebra gln over the complex field C.
基金Royal Society University Research Fellowship(URFR1221398)ERC Starting Grant(project101164551,GeoFEM)Royal Society International Exchanges Grant(IECNSFC233594)资助。
文摘本文围绕内蕴有限元,探讨其在数值偏微分方程中的应用,及其与离散微分几何和拓扑数据分析的潜在联系.由保持连续问题的数学与物理结构的数值离散驱动,本文简要回顾有限元外微分(Finite Element Exterior Calculus,FEEC)的发展.通过经典de Rham复形及BGG复形的规范离散,提出一个扩展的形式值微分形式有限元周期表,涵盖Whitney形式、分布有限元、Regge有限元及Hessian和divdiv复形等,为张量问题的数值求解提供统一工具.本文进一步分析内蕴有限元在Riemann-Cartan几何、广义连续介质及引力波计算等跨学科应用中的潜力.
