Free Product Structure of a Graph W*-probability space
arXiv:math/0507095
Abstract
In this paper, we observe the amalgamated free product structure of a Graph W*-probability space. In [16] and [17], we already observed the operator-valued freeness conditions on a graph W*-algebra. By using the conditions, we will consider the amalgamated free product structure of a graph W*-algebra. In particular, we can make the algebra be blocked, by so-called the loop free blocks (D_G-semicircular blocks) and non-loop blocks (R-diagonal blocks). Finally, we can see the the graph W*-algebra is the free product of edge blocks of the algebra.
29 pages
References in corpus (6)
- Free Semigroupoid Algebras
- Ideal Structure in Free Semigroupoid Algebras from Directed Graphs
- Compatibility of a noncommutative probability space and a noncommutative probability space with amalgamation
- Graph W*-probability Theory
- Random Variables in Graph W*-Probability Spaces
- Amalgamated R-diagonal Pairs