Quaternionic complexes. (English) Zbl 0764.53022

Baston, R. J.

J. Geom. Phys. 8, No. 1-4, 29-52 (1992).

The author studies a quaternion analogue of Dolbeault cohomology obtained by extending the Moisil-Fueter operator from quaternion analysis to a locally exact complex. He uses some Bernstein-Gelfand-Gelfand complexes in representation theory, the Penrose transform and the twistor theory of quaternionic manifolds. The obtained complexes correspond to the semiregular orbits of the Weyl group of \(\text{sl}(2n+2,\mathbb{C})\). In the hyper-Kähler case the author computes the index of these complexes showing that the obtained quaternion cohomology is not trivial.

Reviewer: V.Oproiu (Iaşi)

MSC:

53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
55N30	Sheaf cohomology in algebraic topology
32C35	Analytic sheaves and cohomology groups

Keywords:

Dolbeault cohomology; Moisil-Fueter operator; Bernstein-Gelfand-Gelfand complexes; quaternion cohomology

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