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We describe the absolute retracts for the following classes of finitelattices: (1) slim semimodular lattices, (2) finite distributive lattices, andfor each positive integer $n$, (3) at most $n$-dimensional finite distributivelattices. Although the singleton lattice is the only absolute retract for thefirst class, this result has paved the way to some other classes. For thesecond class, we prove that the absolute retracts are exactly the finiteboolean lattices; this generalizes a 1979 result of J. Schmid. For the thirdclass, the absolute retracts are the finite boolean lattices of dimension atmost $n$ and the direct products of $n$ nontrivial finite chains. Also, wepoint out that in each of these classes, the algebraically closed lattices andthe strongly algebraically closed lattices are the same as the absoluteretracts.  Slim (and necessarily planar) semimodular lattices were introduced by G.Gr\"atzer and E. Knapp in 2007, and they have been intensively studied sincethen. Algebraically closed and strongly algebraically closed lattices have beeninvestigated by J. Schmid and, in several papers, by A. Molkhasi.

Absolute retracts for finite distributive lattices and slim semimodular lattices