Kernels and cokernels in the category of augmented involutive stereotype algebras

Abstract

<jats:p> We prove several properties of kernels and cokernels in the category of augmented involutive stereotype algebras: (1) this category has kernels and cokernels, (2) the cokernel is preserved under the passage to the group stereotype algebras, and (3) the notion of cokernel allows to prove that the continuous envelope [Formula: see text] of the group algebra of a compact buildup of an abelian locally compact group is an involutive Hopf algebra in the category of stereotype spaces [Formula: see text]. The last result plays an important role in the generalization of the Pontryagin duality for arbitrary Moore groups. </jats:p>

On continuous duality for Moore groups

“…Theorem 1.6. 6 Each Lie-Moore group G is a finite extension of some compact buildup of an abelian group.…”

“…Here we correct the error that was made in [11] (and repeated in [5]) with the help of the results of the author's paper [6].…”

“…Proof. We use here Corollary 2.2 from [6], according to which Env C C ⋆ (N ) is a locally convex projective limit of the quotient spaces C ⋆ (N )/p, where p ∈ P(N ):…”

“…(37) Proof. We use here the fact that this proposition was proved in [6] for the special case when G is a compact buildup of an abelian group [6,Theorem 2.8].…”