The letter ℘: name and origin? (2017)

There is an old convention in physics - from the time when Germany was world-leading in physics - to write vector-valued variables in Fraktur. Using cursive (old German cursive is weird) seems related, though AFAIU the "vectorness" of the ℘ function is just the two components of a complex number.

And algebraists often use lowercase fractur for ideals.