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In [6] and [7], we introduced graph von Neumann algebras which are the (groupoid) crossed product algebras of von Neumann algebras and graph groupoids via groupoid actions. We showed that such crossed product algebras have the graph-depending amalgamated reduced free probabilistic properties. In this paper, we will consider a scalarvalued W¤-probability on a given graph von Neumann algebra. We show that a diagonal graph W*-probability space (as a scalar-valued W¤-probability space) and a graph W*-probability space (as an amalgamated W*-probability space) are compatible. By this compatibility, we can find the relation between amalgamated free distributions and scalar-valued free distributions on a graph von Neumann algebra. Under this compatibility,we observe the scalar-valued freeness on a graph von Neumann algebra.
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참고문헌 (32)
참고문헌 신청
A. G. Myasnikov / 2004 / Group Theory, Statistics and Cryptography, Contemporary Mathematics, 360 / American Mathematical Society
A. Nica / / R-diagonal Pair?A Common Approach to Haar Unitaries and Circular Elements
A. Nica / / R-transform in Free Probability, IHP course note
A. Nica / 2002 / R-cyclic families of matrices in free probability / J. Funct. Anal. 188 (1) : 227 ~ 271
B. Bollob´as / 1998 / Modern Graph Theory, Graduate Texts in Mathematics, 184 / Springer-Verlag
A. Nica / / R-diagonal Pair?A Common Approach to Haar Unitaries and Circular Elements
A. Nica / / R-transform in Free Probability, IHP course note
A. Nica / 2002 / R-cyclic families of matrices in free probability / J. Funct. Anal. 188 (1) : 227 ~ 271
B. Bollob´as / 1998 / Modern Graph Theory, Graduate Texts in Mathematics, 184 / Springer-Verlag
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