Left Cauchy–Riemann operator and Dolbeault–Grothendieck lemma on the group of Heisenberg type

Abstract

We extend to differential forms the system of partial differential equations defined for functions as followsThis leads to the cohomology, and then we will prove the corresponding Dolbeault–Grothendieck lemma.

Keywords:

• group of Heisenberg type ℍ_n^B(ℂ)
• left Cauchy–Riemann operator ∂_ℍ^l
• the ∂_ℍ^l¯cohomology

AMS Subject Classifications:

• Primary: 54C40
• 53C56
• Secondary: 32D20
• 32D26

Acknowledgments

The authors are grateful to the anonymous referee for a careful checking of the details and for helpful comments that improved this paper.