The coalgebra of the free difference quotient and free probability

By D. Voiculescu. 2000

124 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e2503e1224d2d0df9fa1cf030161d4bddb87e7ab

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Citations in the corpus

Free analysis questions II: The Grassmannian completion and the series expansions at the origin (2008, background): “One reason is the duality transform for the coalgebra of the free di¤erence quotient ([16] see also [15]).”
The arithmetic of distributions in free probability theory (2005, background): “About the existence and uniqueness of the subordinating functions Z1 and Z2 see also [49, 50].”
Free Probability and Random Matrices (2014, methodology): “However, there is also a subordination version for the operator-valued case which was treated by Biane [13] and, more conceptually, by Voiculescu [48].”
Free Entropy (2001, result): “This leads to a class of coalgebras where the comultiplication is a derivation, which has remarkable duality properties closely related to results on conjugate variables J(X : B); see [55].”
Free analysis questions I: duality transform for the coalgebra of ∂X:B (2004, methodology): “In [12], we also took a look at the coalgebra for which the comultiplication is a derivation (GDQ—generalized difference quotient rings) and found that algebraically, the class has the remarkable property of being self-dual, i.”
Foundations of Free Noncommutative Function Theory (2012, background): “[106] D.-V. Voiculescu.”
Eigenvalues of non-hermitian random matrices and Brown measure of non-normal operators: hermitian reduction and linearization method (2015, methodology): “In order to be able to encapsulate all that inf ormation and efficiently manipulate it, we will use the so-called fully ma tricial extension [35] of GX : GX⊗1n(b) = (E⊗ IdMn) [ (b−X ⊗ 1n) ] ,”