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A description of amalgamated free products of finite von Neumann algebras over finite‐dimensional subalgebras
Author(s) -
Dykema Ken
Publication year - 2011
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdq079
Subject(s) - mathematics , free product , von neumann architecture , subalgebra , free probability , von neumann algebra , tomita–takesaki theory , abelian von neumann algebra , pure mathematics , affiliated operator , class (philosophy) , finitely generated abelian group , algebra over a field , group (periodic table) , jordan algebra , algebra representation , chemistry , organic chemistry , artificial intelligence , computer science
We show that a free product of a II 1 ‐factor and a finite von Neumann algebra with amalgamation over a finite‐dimensional subalgebra is always a II 1 ‐factor, and provide an algorithm for describing it in terms of free products (with amalgamation over the scalars) and compression/dilation. As an application, we show that the class of direct sums of finitely many von Neumann algebras that are interpolated free group factors, hyperfinite II 1 ‐factors, type I n algebras for n finite and finite‐dimensional algebras, is closed under taking free products with amalgamation over finite‐dimensional subalgebras.