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

  • Harsh V Pittie


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.


Compact lie group complex manifold lie algebra cohomology spectral sequence 


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Copyright information

© Indian Academy of Sciences 1988

Authors and Affiliations

  • Harsh V Pittie
    • 1
  1. 1.Department of MathematicsDuke UniversityDurhamUSA

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