seminar at SISSA

[Emanuele Tuillier Illingworth]

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MATHEMATICAL PHYSICS SECTOR SEMINARS
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Piotr M. Hajac
(IMPAN, Warsaw)

will hold a seminar on:
THE PETER-WEYL-GALOIS THEORY OF COMPACT PRINCIPAL BUNDLES


Wednesday, June 25, 14:30, room D, SISSA


Abstract:
The main result is that the freeness of actions of compact quantum
groups
on unital C*-algebras, or more generally, the principality of
comodule
algebras, is preserved under one-surjective pullbacks (fibre
products). We
algebraize the C*-setting by defining for any compact quantum group
action
on a unital C*-algebra its Peter-Weyl comodule algebra. Thus we
extend the
notion of the algebra of regular functions (spanned by the matrix
coefficients of the irreducible unitary corepresentations) from
compact
quantum groups to unital C*-algebras on which they act. This talk
will be
focused on deducing the equivalence of the freeness of a classical
compact
group action on a compact Hausdorff space and the Galois condition
for its
Peter-Weyl comodule algebra. In this way, the well-known analogy
between
coverings and Galois extensions is made precise and generalized from
finite to all compact groups. Time permitting, there will be
entertainment
part explainig how all the above is linked with the the celebrated
Dedekind problem of determining the number of elements in a free
distributive lattice generated by N elements. The problem remains
open
since 1897. (Based on joint work with P.F.Baum, U.Kraehmer,
R.Matthes,
E.Wagner and B.Zielinski.)