  Bialkowski, Erdmann and Skowronski classified those indecomposable
self-injective algebras for which the Nakayama shift of every (non-projective)
simple module is isomorphic to its third syzygy. It turned out that these are
precisely the deformations, in a suitable sense, of preprojective algebras
associated to the simply laced ADE Dynkin diagrams and of another graph L_n,
which also occurs in the Happel-Preiser-Ringel classification of subadditive
but not additive functions. In this paper we study these deformed preprojective
algebras of type L via their Kuelshammer spaces, for which we give precise
formulae for their dimensions. These are known to be invariants of the derived
module category, and even invariants under stable equivalences of Morita type.
As main application of our study of Kuelshammer spaces we can distinguish many
(but not all) deformations of the preprojective algebra of type L up to stable
equivalence of Morita type, and hence also up to derived equivalence.
