Index
C∗-algebra, 122
commutative, 122
Cuntz-Krieger, 129
graph, 129, 146
nuclear, 137, 154
of a bitstream, 147
reduced group, 131
universal group, 131
C∗-bialgebra, 43
algebraic probability space, 29, 87
algebraic quantum group, 45
almost uniform convergence
bilateral, 167
amenability, 157
anti-monotone
independence, 92, 101
L ́evy process, 101
product, 92
antipode
of a dual group, 100
of a Hopf algebra, 32
unitary, 48
automorphism, 124
inner, 124, 152
bialgebra
involutive, 31
Bloch sphere, 8
boolean
independence, 73, 74, 92, 101
L ́evy process, 101
product, 92
Bose independence, 31, 90
Cauchy–Stieltjes transform, 55
reciprocal, 56
coboundary, 36, 40
cocycle, 36,
cogroup, 100
collapse postulate, 6
compact quantum group, 44
of Kac type, 48
compact quantum semigroup, 43
completely positive, 125
compound Poisson process, 40
comultiplication
of a bialgebra, 31
of a dual (semi-)group, 100
conditionally positive, 35
continuous convolution semigroup, 24
contragredient corepresentation, 45
convolution, 23
boolean
additive, 78
multiplicative, 82
free
additive, 57
multiplicative, 59
monotone
additive, 65
multiplicative, 68, 72
of algebra homomorphisms, 100
of linear maps, 31
on a bialgebra, 44
convolution semigroup
of probability measures, 24
of states, 33
coproduct
in a category, 84