In the study of quantum deformations of Witt and Virasoro algebras, the notion of a Hom-Lie algebra first appeared, so is deformation theory insufficient to justify how algebraic structures such as Lie-algebras, ... are deformed, which requires the intervention of the concept of ''Hom'' to define the concepts that have recently appeared, such as Hom-groups...with reasoning ?
Of course questions like this continue to be trendy in mathematical physics,
I dont see any central importance in algebra or physics yet. Lie algebra is central in the
non commutivity of operators in QM, and far reaching hard things like indefinitness.
Things like Virasoro algebra stand out as exotic
so far, irrelevant in normal QM.
The essential structure on noncommutivity, Lie algebra, stands on its own.
Its just a natural property, no exterior aide.
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