The Hochschild cohomology ring of preprojective algebras of type Ln

We compute the Hochschild cohomology of the preprojective algebra of generalized Dynkin type Ln over any commutative ring in which 2 is invertible. In particular, we describe the bigraded ring structure of the Hochschild cohomology ring under the Yoneda product by giving an explicit presentation by homogeneous generators and relations.