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 $\mathbb{C}^n \rtimes_\rho \mathbb{C}$ by a lattice. We discuss their de Rham and Dolbeault cohomology, with emphasis on the degeneration of the Fr\"olicher spectral sequence and the $\partial\bar{\partial}$-Lemma, and their deformations. Finally, we describe their automorphism group in detail.