Some new results on the Chu duality of discrete groups

非阿贝尔局部紧群的Bohr紧化与Chu对偶

Bohr compactification and Chu duality of non-abelian locally compact groups

本研究聚焦非阿贝尔局部紧群的Bohr紧化，刻画其Bohr紧化与Chu对偶或酉拟对偶拓扑同构的条件，修正了文献中部分错误结论。

Pontryagin duality between compact and discrete abelian inverse monoids

For a topological monoid S the dual inverse monoid is the topological monoid of all identity preserving homomorphisms from S to the circle with attached zero. A topological monoid S is defined to be reflexive if the canonical homomorphism from S to its second dual inverse monoid is a topological isomorphism. We prove that a (compact or discrete) topological inverse monoid S is reflexive (if and) only if S is abelian and the idempotent semilattice of S is zero-dimensional. For a discrete (resp. compact) topological monoid its dual inverse monoid is compact (resp. discrete). These results unify …

Representative functions on discrete groupoids and duality with Hopf algebroids

The aim of this paper is to establish a duality between the category of discrete groupoids and the category of geometrically transitive commutative Hopf algebroids in the sense of P. Deligne and A. Bruguières. In one direction we have the usual contravariant functor which assigns to each Hopf algebroid its characters groupoid (the fiber groupoid at the ground field). In the other direction we construct the contravariant functor which associated to each discrete groupoid its Hopf algebroid of representative functions. This duality extends the well known duality between discrete groups and commu…