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Article Dans Une Revue Journal of the London Mathematical Society Année : 2017

Matrix models for noncommutative algebraic manifolds

Résumé

We discuss the notion of matrix model, pi : C(X) -> M-K(C(T)), for algebraic submanifolds of the free complex sphere, X subset of S-C,+(N-1) When K is an element of N is fixed there is a universal such model, which factorizes as pi : C(X) -> C(X-(K)) subset of M-K(C(T)). We have X-(1) = X-class and, under a mild assumption, inclusions X-(1) subset of X-(2) subset of X-(3) subset of ... subset of X. Our main results concern X-(2), X-(3), X-(4),..., their relation with various half-classical versions of X, and lead to the construction of families of higher half-liberations of the complex spheres and of the unitary groups, all having faithful matrix models.

Dates et versions

hal-01898700 , version 1 (18-10-2018)

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Teodor Banica, Julien Bichon. Matrix models for noncommutative algebraic manifolds. Journal of the London Mathematical Society, 2017, 95 (2), pp.519-540. ⟨10.1112/jlms.12020⟩. ⟨hal-01898700⟩
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