Free Analysis Questions I: Duality Transform for the Coalgebra of ∂_X:B

2003/06/10 by Dan Voiculescu, Voiculescu, Dan
Mathematics · #30E99 #30G30 #46L54 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Primary 16W30 #Quantum Algebra (math.QA) #Secondary 47C05 #math.OA #math.QA #msc:16W30 #msc:30E99 #msc:30G30 #msc:46L54 #msc:47C05

paper · pdf · doi:10.48550/arxiv.math/0306172

27 pages; key words and phrases: free difference quotient, derivation-comultiplication, generalized matricial resolvent, coalgebra duality, free

arxiv created 2003/06/10 · openalex publication_date 2003/06/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A duality transform for the coalgebra of the free difference quotient derivation-multiplication of an operator with respect to a free algebra of scalars is constructed. The dual object is realized in an algebra of matricial analytic functions endowed with yet another generalization of the difference quotient derivation.

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