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Dimension-Drop Algebra

A dimension-drop algebra I(p,q), for positive integers p,q, is the C*-algebra

I(p,q)={f in C([0,1],M_p(C) tensor M_q(C)):f(0) in M_p(C) tensor 1_q, f(1) in 1_p tensor M_q(C)}.

The endpoint conditions reduce the matrix dimensions there, while an interior evaluation has matrix size pq. When p,q are relatively prime, it is called a prime dimension-drop algebra. These algebras are building blocks for the Jiang-Su algebra.

See also

C*-Algebra, C*-Algebra Character, C*-Algebra Tensor Product, Jiang-Su Algebra, Jiang-Su Stability

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References

Rørdam, M. and Winter, W. "The Jiang-Su Algebra Revisited." J. reine angew. Math. 642, 129-155, 2010. https://doi.org/10.1515/crelle.2010.039.

Cite this as:

Weisstein, Eric W. "Dimension-Drop Algebra." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Dimension-DropAlgebra.html

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