You can only install extensions that are already built into the PostgreSQL image we use (supabase/postgres:latest).
Based on that image, the available extensions include:
amcheck, autoinc, bloom, btree_gin, btree_gist, citext, cube, dblink, dict_int, dict_xsyn, earthdistance, file_fdw, fuzzystrmatch, hstore, insert_username, intagg, intarray, isn, lo, ltree, moddatetime, pgcrypto, plpgsql, uuid-ossp, and several others.
If you need an extension not included in this list, we would need to use a custom database image.
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