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quantum posets

Journal of the Institute of Mathematics of Jussieu (1)

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1 results

HEREDITARILY ANTISYMMETRIC OPERATOR ALGEBRAS
Part of
- Topological (rings and) algebras with an involution
- Ordered sets
Nik Weaver
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 20 / Issue 3 / May 2021

Published online by Cambridge University Press:

09 October 2019, pp. 1039-1074

Print publication:

May 2021
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We introduce a notion of ‘hereditarily antisymmetric’ operator algebras and prove a structure theorem for them in finite dimensions. We also characterize those operator algebras in finite dimensions which can be made upper triangular and prove matrix analogs of the theorems of Dilworth and Mirsky for finite posets. Some partial results are obtained in the infinite dimensional case.