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    • The Dolbeault-cohomology ring of a compact, even-dimensional lie group

      Harsh V Pittie

      Volume 98 Issue 2-3 December 1988 pp 117-152

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/098/02-03/0117-0152

    • Keywords

       

      Compact lie group; complex manifold; lie algebra; cohomology; spectral sequence

    • Abstract

       

      The paper presents a classification of all homogeneous (integrable) complex structures on compact, connected lie groups of even dimension. Thereafter, using lie algebraic methods it proves theorems about the Dolbeault cohomology rings of these complex manifolds in the semisimple case and exhibits the dramatic variation of ring structure of the Dolbeault rings of groups of rank 2. Using some specific computations forSO(9), it gives a counter-example to a long-standing conjecture about the Hodge-deRham (Frohlicher) spectral sequence.

    • Author Affiliations

       

      Harsh V Pittie1

      1. Department of Mathematics, Duke University, Durham, North Carolina - 27706, USA

    • Dates

       
      Published
      December 1988
      Manuscript received
      16 January 1988
      Manuscript revised
      25 June 1988

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