sentence1: the notion of hom-lie algebras was introduced by hartwig , larsson , and silvestrov in as part of a study of deformations of witt algebras and virasoro algebras .
sentence2: this hom-type generalization of algebras appeared as a part of the study of discretizations and deformations of vector fields and differential calculi regarding the effort to deform the witt and the virasoro algebras .