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Co‐representation theory of universal co‐sovereign Hopf algebras
Author(s) -
Bichon Julien
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdl007
Subject(s) - representation theory , mathematics , hopf algebra , pure mathematics , automorphism , representation (politics) , quantum group , algebraically closed field , group (periodic table) , general linear group , algebra over a field , discrete mathematics , symmetric group , quantum mechanics , physics , politics , political science , law
We determine the co‐representation theory of the universal co‐sovereign Hopf algebras, which are some natural analogues of the general linear groups in quantum group theory, for generic matrices over an algebraically closed field of characteristic zero. Our results generalize Banica's previous results in the compact case. As an application, we easily get the representation theory of the quantum automorphism group of a matrix algebra endowed with a non‐necessarily tracial measure.