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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Quasimorphisms and Bavard's duality
拟同构 巴瓦尔 对偶性
2023/4/18
Quasimorphisms are generalizations of homomorphisms to the real number. Groups with nice aciton on Gromov-hyperbolic spaces often have a large space of quasimorphisms, although such groups can have tr...
Duality for Nonlinear Simply Laced Groups
Local Langlands Conjecture nonlinear groups Kazhdan-Lusztig theory
2015/9/28
We establish a character multiplicity duality for a certain natural class of nonlinear (nonalgebraic) groups arising as two-fold covers of simply laced real reductive algebraic groups. This allows us ...
Koszul duality of operads and homology of partition posets
Koszul duality operads homology partition posets
2015/3/25
We consider partitions of a set with r elements ordered by refinement. We consider the simplicial complex Kˉ(r) formed by chains of partitions which starts at the smallest element and ends at the larg...
Koszul duality for Operads
Koszul duality Operads
2015/3/25
This is a copy of the article by the same authors published in Duke Math. J. (1994).
A Koszul duality for props
Koszul duality props
2015/3/25
The notion of prop models the operations with multiple inputs and multiple outpus, acting on some algebraic structures like the bialgebras or the Lie bialgebras. In this paper, we generalize the Koszu...
Manin products, Koszul duality, Loday algebras and Deligne conjecture
Manin products Koszul duality Loday algebras Deligne conjecture
2015/3/25
In this article we give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to associative algebras, non-symmetric o...
During the summer of 1985, after the opening ceremony of Nankai Institute of Mathematics,a beautiful lecture of S.-S. Chern on Chern classes and the Atiyah-Singer index formula introduced me into the ...
We discuss the consequences of the Poincar\'e duality, versus AS- Gorenstein property, for Koszul algebras (homogeneous and non homogeneous). For homogeneous Koszul algebras, the Poincar\'e duality pr...
Super duality and homology of unitarizable modules of Lie algebras
Super duality homology of unitarizable modules of Lie algebras
2011/1/18
The u-homology formulas for unitarizable modules at negative levels over classical Lie algebras of infinite rank of types gl(n), sp(2n) and so(2n) are obtained.As a consequence, we recover the Enright...
Finite $W$-superalgebras for queer Lie superalgebras and higher Sergeev duality
Finite $W$-superalgebras queer Lie superalgebras higher Sergeev duality
2011/1/20
We initiate and develop the theory of finite W-superalgebras W associated to the queer Lie superalgebra g = q(N) and a nilpotent linear func-tional ∈ g ¯0 . We show that the definition of th...
Duality for cochain DG algebras
Balanced dualizing complex Castelnuovo-Mumford re-gularity
2011/2/22
This paper develops a duality theory for connected cochain DG algebras, with particular emphasis on the non-com-mutative aspects.
On duality and negative dimensions in the theory of Lie groups and symmetric spaces
duality negative dimensions theory Lie groups symmetric spaces
2010/11/8
We give one more interpretation of the symbolic formulae $U(-N)=U(N)$ and $Sp(-2N)=SO(2N)$ by comparing the values of certain Casimir operators in the corresponding tensor representations. We show al...
Extremal maps in best constants vector theory - Part I: Duality and Compactness
Extremal maps constants vector theory - Part I
2010/11/11
We develop a comprehensive study on sharp potential type Riemannian Sobolev inequalities of order 2 by means of a local geometric Sobolev inequality of same kind and suitable De Giorgi-Nash-Moser est...
K-Theoretic Duality for Hyperbolic Dynamical Systems
K-Theoretic Duality Hyperbolic Dynamical Systems
2010/12/13
The K-theoretic analog of Spanier-Whitehead duality for noncommutative C-algebras is shown to hold for the Ruelle algebras associated to irreducible Smale spaces.This had previously been proved only ...
An Algebraic Duality Theory for Multiplicative Unitaries
Algebraic Duality Theory Multiplicative Unitaries
2010/10/29
Multiplicative Unitaries are described in terms of a pair of commuting shifts of relative depth two. They can be generated from ambidextrous Hilbert spaces in a tensor C*-category. The algebraic anal...