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Factor Fundamental Group

The fundamental group of a type II_1 von Neumann factor M is the multiplicative subgroup

F(M)={t>0:M^t=M},

where M^t is its amplification using a projection of unnormalized matrix trace t. This is an invariant of the operator algebra, distinct from the topological fundamental group. For example, 1 always belongs to F(M).

See also

Fundamental Group, Twisted Group von Neumann Algebra, von Neumann Factor

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References

Anantharaman, C. and Popa, S. An Introduction to II_1 Factors. https://www.math.ucla.edu/~popa/Books/IIun.pdf.

Cite this as:

Weisstein, Eric W. "Factor Fundamental Group." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FactorFundamentalGroup.html

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