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HEREDITARILY ANTISYMMETRIC OPERATOR ALGEBRAS

Part of: Topological (rings and) algebras with an involution Ordered sets

Published online by Cambridge University Press:  09 October 2019

Nik Weaver Open the ORCID record for Nik Weaver [Opens in a new window]
Nik Weaver*
Affiliation:
Department of Mathematics, Washington University in Saint Louis, Saint Louis, MO63130, USA ([email protected])
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Abstract

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.

Keywords

antisymmetric operator algebrasquantum posets

MSC classification

Primary: 46K50: Nonselfadjoint (sub)algebras in algebras with involution
Secondary: 06A75: Generalizations of ordered sets
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 3 , May 2021 , pp. 1039 - 1074
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Copyright
© Cambridge University Press 2019

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