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00048487 Gundlach, Markus \"Uber die Kohomologie nilpotenter Lie-Algebren und nilpotenter Gitter. (On the cohomology of nilpotent Lie algebras and nilpotent lattices). D\"usseldorf: Univ. D\"usseldorf, Math.-Naturwiss. Fak., Diss. 67 S. (1990). 1990 D\"usseldorf: Univ. D\"usseldorf, Math.-Naturwiss. Fak. DE cohomology nilpotent Lie algebra lattice connected nilpotent Lie group The dissertation under review consists of two independent parts. Chapter 1 deals with the cohomology of a nilpotent Lie algebra over a commutative ring R which is defined to be a Lie algebra ${\frak g}$ with a series of central extensions $R\to {\frak g}\sp{i+1}\to {\frak g}\sp i$ such that ${\frak g}\sp 1=R$ and ${\frak g}\sp n={\frak g}$. It is proved that nilpotency $\Rightarrow$ every cocycle is presented by a defining system (a notion related to the Massey product of cohomology classes, for precise definition see the dissertation itself) $\Rightarrow$ every 2- coboundary is presented by a defining system $\Rightarrow$ the existence of a faithful representation by proper upper triangular matrices $\Rightarrow$ the descending central series descends to zero. When R is a field these implications are really equivalences, but in general they are not. Chapter 2 concerns the cohomology of a lattice $\Gamma$ in a connected nilpotent Lie group G (i.e., $\Gamma$ is a discrete subgroup of G such that G/$\Gamma$ is compact). An algorithm to determine the second cohomology group $H\sp 2(\Gamma)$ is concretely given. An estimation of the nilpotency index of $\Gamma$ through the cup product of elements of $H\sp 2(\Gamma)$ is obtained. Shen Guangyu (Shanghai)