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The Locally Finite Part of the Dual Coalgebra of Quantized Irreducible Flag Manifolds
Author(s) -
Heckenberger I.,
Kolb S.
Publication year - 2004
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611504014777
Subject(s) - mathematics , coalgebra , pure mathematics , flag (linear algebra) , duality (order theory) , covariant transformation , dual (grammatical number) , vector space , generalized flag variety , algebra over a field , lie group , mathematical physics , art , literature
For quantized irreducible flag manifolds the locally finite part of the dual coalgebra is shown to coincide with a natural quotient coalgebra U ¯ of U q g . On the way the coradical filtration of U ¯ is determined. A graded version of the duality between U ¯ and the quantized coordinate ring is established. This leads to a natural construction of several examples of quantized vector spaces. As an application, covariant first order differential calculi on quantized irreducible flag manifolds are classified. 2000 Mathematics Subject Classification 58B32 (primary), 81R50 (secondary).