Free Subproducts and Free Scaled Products of II1-Factors
نویسندگان
چکیده
منابع مشابه
Free Subproducts and Free Scaled Products of Ii1–factors
The constructions of free subproducts of von Neumann algebras and free scaled products are introduced, and results about them are proved, including rescaling results and results about free trade in free scaled products.
متن کاملRescalings of Free Products of Ii1–factors
We introduce the notation Q(1) ∗ · · · ∗ Q(n) ∗L(Fr) for von Neumann algebra II1–factors where r is allowed to be negative. This notation is defined by rescalings of free products of II1–factors, and is proved to be consistent with known results and natural operations. We also give two statements which we prove are equivalent to isomorphism of free group factors.
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Let Q be any II1–factor. It is shown that any standard lattice G can be realized as the standard invariant of a free product of (several) rescalings of Q. In particular, if Q has fundamental group equal to the positive reals and if P is the free product of infinitely many copies of Q, then P has subfactors giving rise to all possible standard invariants. Similarly, given a II1–subfactor N ⊂ M ,...
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In this work, I address a primary issue with adapting categorical and algebraic concepts to functional analytic settings, the lack of free objects. Using a “normed set” and associated categories, I describe constructions of normed objects, which build from a set to a vector space to an algebra, and thus parallel the natural progression found in algebraic settings. Each of these is characterized...
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In this paper, we verify the solvability of free product of finite cyclic groups with topological methods. We use Cayley graphs and Everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator subgroups. In particular, using these methods, we prove that the commutator subgroup of $mathbb{Z}_{m}*mathbb{Z}_{n}$ is free of rank $(m-1)(n-1)$ fo...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2002
ISSN: 0022-1236
DOI: 10.1006/jfan.2002.3948