Haar measure and the semigroup of measures on a compact group

Haar Measure and the Semigroup of Measures on a Compact Group

The Haar Measure on a Compact Quantum Group

Let A be a C*-algebra with an identity. Consider the completed tensor product A®A of A with itself with respect to the minimal or the maximal C*-tensor product norm. Assume that A: A —>A®A is a non-zero •-homomorphism such that (A ® t)A = (i ® A)A where / is the identity map. Then A is called a comultiplication on A . The pair (A, A) can be thought of as a 'compact quantum semi-group'. A left i...

Conditional Haar Measures on Classical Compact Groups

We give a probabilistic proof of the Weyl integration formula on U(n), the unitary group with dimension n. This relies on a suitable definition of Haar measures conditioned to the existence of a stable subspace with any given dimension p. The developed method leads to the following result: for this conditional measure, writing Z (p) U for the first nonzero derivative of the characteristic polyn...

The Semigroup of Compact Metric Measure Spaces and Its Infinitely Divisible Probability Measures

A compact metric measure space is a compact metric space equipped with probability measure that has full support. Two such spaces are equivalent if they are isometric as metric spaces via an isometry that maps the probability measure on the first space to the probability measure on the second. The resulting set of equivalence classes can be metrized with the GromovProhorov metric of Greven, Pfa...

The Haar measure on some locally compact quantum groups

A locally compact quantum group is a pair (A,Φ) of a C-algebra A and a -homomorphism Φ from A to the multiplier algebra M(A ⊗ A) of the minimal C-tensor product A ⊗ A satisfying certain assumptions (see [K-V1] and [K-V2]). One of the assumptions is the existence of the Haar weights. These are densely defined, lower semi-continuous faithful KMS-weights satisfying the correct invariance propertie...