Split Nakamura manifolds and their automorphisms

In this paper we study the class of \emph{split Nakamura manifolds}, which are a type of solvmanifolds generalizing Nakamura’s threefold, defined as quotients of the semidirect product ${\mathbb{C}}^n{⋊}_{\rho }\mathbb{C}$ by a lattice. We discuss their de Rham and Dolbeault cohomology, with emphasis on the degeneration of the Frölicher spectral sequence and the $\mathrm{\partial }\bar{\mathrm{\partial }}$-Lemma, and their deformations. Finally, we describe their automorphism group in detail.