The locally finite part of the dual coalgebra of quantized irreducible flag manifolds

• Autores: I. Heckenberger, S. Kolb
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 89, Nº 2, 2004, págs. 457-484
• Idioma: inglés
• DOI: 10.1112/s0024611504014777
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• Resumen

  • For quantized irreducible flag manifolds the locally finite part of the dual coalgebra is shown to coincide with a natural quotient coalgebra $\overline{U}$ of $U_q ( \mathfrak{g} )$. On the way the coradical filtration of $\overline{U}$ is determined. A graded version of the duality between $\overline{U}$ 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.