Unitarization of linear representations of non-primitive posets

2009/11/22 by Roman Grushevoi, Grushevoi, Roman, Kostyantyn Yusenko +1
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #Representation Theory (math.RT) #math.OA #math.RT

paper · pdf · doi:10.48550/arxiv.0911.4237

32 pages, Several Appendix are added. Proofs completed. Several typos were fixed

arxiv created 2010/06/16 · arxiv updated 2010/06/17

Abstract

We prove that partially ordered set has finite number of finite-dimensional indecomposable nonequivalent Hilbert representations with orthoscalarity condition if and anly if it has finite number of indecomposable linear representations. We show that each indecomposable representation of the poset of finite type could be unitarized with some weight.

Related

• Some remarks on Hilbert representations of posets
• Stable representations of posets
• Kleiner's theorem for unitary representations of posets
• N-free posets and orthomodularity
• Orthomodular and generalized orthomodular posets