2010/12/20 by Rodrigo Vargas Le-Bert, Le-Bert, Rodrigo Vargas · 1 citation
Mathematics · #16S #46L #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.OA #math.RA #math.RT #msc:16S #msc:46L
paper · pdf · doi:10.48550/arxiv.1012.4435
Final version, to be published in Algebras and Representation Theory. Section 2 shortened, proof of Corollary 3.11 (now 3.12) corrected, and other minor changes
openalex publication_date 2010/12/20 · arxiv created 2011/04/13 · arxiv updated 2011/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathcal A be a unital algebra equipped with an involution (⋅)^†, and suppose that the multiplicative set \mathcal S⊆ \mathcal A generated by the elements of the form 1 + a^† a satisfies the Ore condition. We prove that: (i) Cyclic representations of \mathcal A admit an integrable extension (acting on a possibly larger Hilbert space), and (ii) Integrable representations of \mathcal A are in bijection with representations of the Ore localization \mathcal A\mathcal S-1 (which we prove to be an involutive algebra). This second result is a limited converse to a theorem by Inoue asserting that representations of symmetric involutive algebras are integrable.