Algebras in Plancherel duality and algebraic combinatorics
type: Item
instance of: scholarly article
title: Algebras in Plancherel duality and algebraic combinatorics
zbMATH Open document ID: 0917.16006
DOI: 10.1007/BF02466057
publication date: 1999-06-13T00:00:00Z
review text: The authors consider finite-dimensional *-algebras over \(\mathbb{C}\). Such an algebra is called a \(C\)-algebra, if it has a vector space basis \(R\) satisfying several given conditions (expressed in terms of so-called structure constants). The main result states that the category of positive \(C\)-algebras is equivalent to a (suitably defined) category of pairs of algebras in Plancherel duality. The authors also indicate some relations between the concepts considered and some generalizations of Hopf algebras which they are going consider in a subsequent publication.
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 46B10
Mathematics Subject Classification ID: 46K05
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 1226005
zbMATH Keywords: finite-dimensional *-algebras
zbMATH Keywords: categories of pairs of algebras
zbMATH Keywords: Plancherel duality
zbMATH Keywords: generalizations of Hopf algebras
zbMATH Keywords: categories of positive \(C\)-algebras
author: S. A. Evdokimov
author: Ilya Ponomarenko
author: A. M. Vershik
reviewed by: Wiesław Tadeusz Żelazko
MaRDI profile type: Publication
cites work: Q3218140
cites work: Combinatorial algebras and multivalued involutive groups
cites work: \(C\)-algebras and algebras in Plancherel duality
cites work: Coherent algebras
cites work: Q4042153
cites work: On construction and identification of graphs. With contributions by A. Lehman, G. M. Adelson-Velsky, V. Arlazarov, I. Faragev, A. Uskov, I. Zuev, M. Rosenfeld and B. Weisfeiler
full work available at URL: https://doi.org/10.1007/bf02466057
OpenAlex ID: W2094566800
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1226005