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

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Emmanuel Germain
Non-commutative entropy computations for continuous fields and cross-products
(Calculs d’entropie non commutative pour des champs continus ou des produits croisés)
Annales mathématiques Blaise Pascal, 14 no. 1 (2007), p. 1-16, doi: 10.5802/ambp.223
Article PDF | Reviews MR 2298720 | Zbl 1132.46041
Class. Math.: 46L55, 46L53
Keywords: non-commutative dynamical entropy, cross-products, continuous fields

Résumé - Abstract

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 $C(X)$-automorphisms. Each result relies on explicit factorization via matrices.

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