Non-commutative entropy computations for continuous fields and cross-products

Germain, Emmanuel

Annales mathématiques Blaise Pascal, Tome 14 (2007) no. 1, pp. 1-16.

Nous présentons deux situations de géométrie non commutative dans lesquelles des calculs d’entropie dynamique non commutative sont possibles. La première s’interesse aux automorphismes des produits croisés par un groupe exact qui commutent avec l’action du groupe généralisant un résultat connu pour les groupes moyennables. La seconde concerne les champs continues de $C^{*}$-algèbres et les automorphismes fibrés. Dans chacun des deux cas, il s’agit d’utiliser des factorisations explicites par des algèbres de matrices.

We present here two non-commutative situations where dynamical entropy estimates are possible. The first result is concerned with automorphisms of cross-products by an exact group that commute with the group action and generalizes the result known for amenable groups. The second is about continuous fields of C${}^{*}$-algebras and $C\left(X\right)$-automorphisms. Each result relies on explicit factorization via matrices.

Classification : 46L55, 46L53
Keywords: non-commutative dynamical entropy, cross-products, continuous fields
Mot clés : entropie dynamique non commutative, produits croisés, champs continus

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