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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...
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 ...
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...
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...
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...
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...
This paper develops a duality theory for connected cochain DG algebras, with particular emphasis on the non-com-mutative aspects.
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...
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...
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 ...
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...

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