Homomorphism reductions on Polish groups

On homomorphism spaces of metrizable groups

For two not necessarily commutative topological groups G and T , let H(G, T ) denote the space of all continuous homomorphisms from G to T with the compact-open topology. We prove that if G is metrizable and T is compact then H(G, T ) is a k-space. As a consequence we obtain that if G1 is a dense subgroup of G then H(G1, T ) is homeomorphic to H(G,T ), and if G is separable h-complete, then the...

On minimal actions of Polish groups

We show the existence of an infinite monothetic Polish topological group G with the fixed point on compacta property. Such a group provides a positive answer to a question of Mitchell who asked whether such groups exist, and a negative answer to a problem of R. Ellis on the isomorphism of L(G), the universal point transitive G-system (for discrete G this is the same as PG the Stonetech compacti...

On Gauss decomposition of quantum groups and Jimbo homomorphism

It is shown that the properties of the Gauss decomposition of quantum groups and the known Jimbo homomorphism permit us to realize these groups as subalgebras of well defined algebras constructed from generators of the corresponding undeformed Lie algebras. This research was supported by RFFI grants No 97-01-01152. E-mail adress: [email protected] 1. The purpose of this Letter is to show tha...

Anti-Homomorphism in Fuzzy Sub Groups

Anti-Homomorphism in Fuzzy Sub Groups

In this paper, a new concept of anti-homomorphism between two fuzzy groups G and G‫׀‬ is defined many results analogous to homomorphism of groups are established