Lexical Definition

‎ἡγεμονία‎ hēgemonía (hayg-em-on-ee'-ah) reign ^G:N-F
from ‎ἡγεμών‎

reign.

• government, i.e. (in time) official term

Abbott-Smith

ἡγεμονία, -ας, ἡ (< ἡγεμών), [in LXX: Ge 36:30 (אַלּוּף), Nu 1:52 2:17 (דֶּגֶל), Si 7:4 10:1, IV Mac 6:33 13:4*;]
rule, sovereignty: Lk 3:1.†

Abbott-Smith References

Liddell-Scott-Jones

ἡγεμονία-ία, ἡ,

leading the way, going first, [Refs 5th c.BC+]; τῇ τῶν δυναστευόντων ἡ. by their example, [Refs 5th c.BC+]

__II authority, rule, of dynasties or nations, [Refs 5th c.BC+]; of a general or officer, [ἡγεμονίαίαις [prev. author] 7.15 ">Refs 5th c.BC+]; ἡ ἡ. τῶν Ἰώνων τοῦ πολέμου [Refs 5th c.BC+]; ἡ κατὰ πόλεμον ἡ., τῶν πολεμικῶν ἡ ἡ., [Refs 5th c.BC+]; ἡ. δικαστηρίου presidency in a court, [Refs 4th c.BC+]; headship of a philosophical school, [Refs 1st c.BC+]
__II.2 political supremacy, ἡ ἡ. τῆς 'Ελλάδος [Refs 5th c.BC+]; ἡ ἐν 'Αρείῳ πάγῳ βουλὴ οὐδενὶ δόγματι λαβοῦσα τὴν ἡ.[Refs]; political leadership of an individual, [Refs]
__II.2.b = Latin imperium, [ἡγεμονίαίᾳ προσέθηκα “Mon.Anc.Gr.” 15.1; τοῖς καλοῖς τῆς ἡ. νόμοις 2nd c.BC: Athenaeus Mechanicus 39.7 ">Refs 2nd c.BC+]; τριῶν τῶν μεγίστων ἡ. [Refs 1st c.AD+]; reign of an Emperor, [NT]; office of prefect, [Refs 2nd c.AD+]
__III military unit, regiment, [Refs 2nd c.BC+]; but αἱ μείζονες ἡ. the higher commands, [Refs 2nd c.AD+]
__IV chief thing, principal part, ἡ. τῆς τέχνης [Refs 4th c.BC+]
__V a principality, [LXX]; a Roman governorship, ἡ 'Ιλλυρίδος ἡ. [Refs 2nd c.AD+]; tenure of office of a governor, [Refs 2nd c.AD+]; ἡ Ἡ. the Government, [Refs 3rd c.AD+]

_{LSJ Scripture Refs: Luke.3.1 ☩ LXX.Gen.36.30}