C-VALUED FREE PROBABILITY ON A GRAPH VON NEUMANN ALGEBRA
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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.
Abstract
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.
참고문헌 (32)
- B. Bollob´as, "Modern Graph Theory, Graduate Texts in Mathematics, 184" (1998), Springer-Verlag
- I. Cho, "Graph-matrices over additive graph groupoids", Submitted to JAMC
- Ilwoo Cho, "Group-freeness and certain amalgamated freeness", 대한수학회지, 45(3), pp.597~609 (2008), 대한수학회
- Ilwoo Cho, "Direct producted $W^{*}$-probability spaces and corresponding amalgamated free stochastic integration", 대한수학회보, 44(1), pp.131~150 (2007), 대한수학회
- I. Cho, "Measures on graphs and groupoid measures", Complex Anal. Oper. Theory, 2(1), pp.1~28 (2008)
- I. Cho, "Graph von Neumann algebras", Acta Appl. Math., 95(2), pp.95~134 (2007)
- I. Cho, "Characterization of amalgamated free blocks of a graph von Neumann algebra", Complex Anal. Oper. Theory, 1(3), pp.367~398 (2007)
- I. Cho, "Vertex-compressed algebras of a graph von Neumann algebra", Acta Appl. Math. (2008)
- I. Cho, "Operator Algebraic Quotient Structures of Graph von Neumann Algebras" (2008), CAOT
- I. Cho, "C*-algebras generated by partial isometries", JAMC (2008)
- I. Cho, "C*-subalgebras generated by partial isometries", JMP (2008)
- I. Cho, "Applications in automata and graphs: Labeling operators in Hilbert space I", Submitted to Acta Appl. Math: Special Issues (2007)
- I. Cho, "Applications in automata and graphs: Labeling operators in Hilbert space II", Submitted to JMP (2008)
- I. Cho, "C*-subalgebras generated by a single operator in B(H)", Submitted to Acta Appl. Math: Special Issues (2008)
- I. Cho, "C*-dynamical systems induced by partial isometries", ~ (2008)
- R. Diestel, "Graph Theory: 3-rd edition, Graduate Texts in Mathematics, 173" (2005), Springer-Verlag
- R. Exel, "Interaction", ~ (2004)
- R. Exel, "A new look at the crossed-product of a C¤-algebra by an endomorphism", Ergodic Theory Dynam. Systems, 23(6), pp.1733~1750 (2003)
- R. Gliman, "Computational and Statistical Group Theory, Contemporary Mathematics, 298" (2002), American Mathematical Society
- V. F. R. Jones, "Subfactors and Knots, CBMS Regional Conference Series in Mathematics, 80", Published for the Conference Board of the Mathematical Sciences (1991), American Mathematical Society
- M. T. Jury, "Ideal structure in free semigroupoid algebras from directed graphs", J. Operator Theory, 53(2), pp.273~302 (2005)
- A. G. Myasnikov, "Group Theory, Statistics and Cryptography, Contemporary Mathematics, 360" (2004), American Mathematical Society
- A. Nica, "R-cyclic families of matrices in free probability", J. Funct. Anal., 188(1), pp.227~271 (2002)
- F. Rˇadulescu, "Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index", Invent. Math., 115(2), pp.347~389 (1994)
- I. Raeburn, "Graph Algebras, CBMS Regional Conference Series in Mathematics, 103", Published for the Conference Board of the Mathematical Sciences (2005), American Mathematical Society
- B. Solel, "You can see the arrows in a quiver operator algebra", J. Aust. Math. Soc., 77(1), pp.111~122 (2004)
- R. Speicher, "Combinatorial theory of the free product with amalgamation and operatorvalued free probability theory", Mem. Amer. Math. Soc., 132(627), pp.88~ (1998)
- D. Voiculescu, "Operations on certain non-commutative operator-valued random variables", Ast´erisque, (232), pp.243~275 (1995)
- D. Voiculescu, "Free Random Variables" (1992), American Mathematical Society