Let d ≥ 1, and let α be an expansive Z-action by continuous automorphisms of a compact abelian group X with completely positive entropy. Then the group ∆α(X) of homoclinic points of α is countable and dense in X, and the restriction of α to the α-invariant subgroup ∆α(X) is a Z-action by automorphisms of ∆α(X). By duality, there exists a Z-action α∗ by automorphisms of the compact abelian group...

Let X be a compact Hausdorff space and let H be a separable Hilbert space. We prove that the group of all order automorphisms of the C∗-algebra C(X)⊗ B(H) is algebraically reflexive.

B. Harris [5] defined the harmonic volume for the compact Riemann surface X of genus g ≥ 3, using Chen’s iterated integrals [2]. Let J(X) be the Jacobian variety of X. By the Abel-Jacobi map X → J(X), X is embedded in J(X). By a consideration of the special harmonic volume, Harris [6] proved that the algebraic cycle F (4)−F (4) is not algebraically equivalent to zero in J(F (4)). Here, F (4) is...

Alas, the motivating examples of algebraically compact categories are not algebraically compact, and the enriched setting does not directly support the theory of algebraic compactness. We show that the structural setting, the same setting developed independently for models of linear logic, directly supports the theory of algebraic cocompleteness. We extend the structural setting to a bistructur...

We shall extend the results of [5] and prove that if f = Z o a x ? Z [[X]] is algebraic over Q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over Q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over Q (x) if and only if f , f ,.., f are algebraically independent over Q (x)

We call a nitely complete category algebraically coherent if the change-ofbase functors of its bration of points are coherent, which means that they preserve nite limits and jointly strongly epimorphic pairs of arrows. We give examples of categories satisfying this condition; for instance, coherent categories, categories of interest in the sense of Orzech, and (compact) Hausdor algebras over a ...

Abstract. This course introduces classical and new results on the algebraic structure of the identity component of the diffeomorphism group Diff0(M) or homeomorphism group Homeo0(M) of a compact manifold. These groups are algebraically simple (no nontrivial normal subgroups) – for deep topological reasons due to Epstein, Mather, Thurston... but nevertheless have a very rich algebraic structure....

Let G be a compact Lie group and M a closed smooth G manifold. With some restrictions on G or on the isotropy groups of the action we show that M is algebraically realized, i. e., there exists a non-singular real algebraic G variety which is equivariantly diffeomorphic to M .