Question: What dynasty gave birth to the empire that included the Principality of Lüneburg?

full_context: Document 1: Middle Ages: A three-year civil war followed his death. By the Treaty of Verdun (843), a kingdom between the Rhine and Rhone rivers was created for Lothair to go with his lands in Italy, and his imperial title was recognised. Louis the German was in control of Bavaria and the eastern lands in modern-day Germany. Charles the Bald received the western Frankish lands, comprising most of modern-day France. Charlemagne's grandsons and great-grandsons divided their kingdoms between their descendants, eventually causing all internal cohesion to be lost.[N] In 987 the Carolingian dynasty was replaced in the western lands, with the crowning of Hugh Capet (r. 987–996) as king.[O][P] In the eastern lands the dynasty had died out earlier, in 911, with the death of Louis the Child, and the selection of the unrelated Conrad I (r. 911–918) as king.
Document 2: East Prussia: Although Brandenburg was a part of the Holy Roman Empire, the Prussian lands were not within the Holy Roman Empire and were with the administration by the Teutonic Order grandmasters under jurisdiction of the Emperor. In return for supporting Emperor Leopold I in the War of the Spanish Succession, Elector Frederick III was allowed to crown himself "King in Prussia" in 1701. The new kingdom ruled by the Hohenzollern dynasty became known as the Kingdom of Prussia. The designation "Kingdom of Prussia" was gradually applied to the various lands of Brandenburg-Prussia. To differentiate from the larger entity, the former Duchy of Prussia became known as Altpreußen ("Old Prussia"), the province of Prussia, or "East Prussia".
Document 3: Duchy of Magdeburg: The Duchy of Magdeburg () was a province of Margraviate of Brandenburg from 1680 to 1701 and a province of the German Kingdom of Prussia from 1701 to 1807. It replaced the Archbishopric of Magdeburg after its secularization by Brandenburg. The duchy's capitals were Magdeburg and Halle, while Burg was another important town. Dissolved during the Napoleonic Wars in 1807, its territory was made part of the Province of Saxony in 1815.
Document 4: Middle Ages: The coronation of Charlemagne as emperor on Christmas Day 800 is regarded as a turning point in medieval history, marking a return of the Western Roman Empire, since the new emperor ruled over much of the area previously controlled by the western emperors. It also marks a change in Charlemagne's relationship with the Byzantine Empire, as the assumption of the imperial title by the Carolingians asserted their equivalence to the Byzantine state. There were several differences between the newly established Carolingian Empire and both the older Western Roman Empire and the concurrent Byzantine Empire. The Frankish lands were rural in character, with only a few small cities. Most of the people were peasants settled on small farms. Little trade existed and much of that was with the British Isles and Scandinavia, in contrast to the older Roman Empire with its trading networks centred on the Mediterranean. The empire was administered by an itinerant court that travelled with the emperor, as well as approximately 300 imperial officials called counts, who administered the counties the empire had been divided into. Clergy and local bishops served as officials, as well as the imperial officials called missi dominici, who served as roving inspectors and troubleshooters.
Document 5: Greeks: The Eastern Roman Empire – today conventionally named the Byzantine Empire, a name not in use during its own time – became increasingly influenced by Greek culture after the 7th century, when Emperor Heraclius (AD 575 - 641) decided to make Greek the empire's official language. Certainly from then on, but likely earlier, the Roman and Greek cultures were virtually fused into a single Greco-Roman world. Although the Latin West recognized the Eastern Empire's claim to the Roman legacy for several centuries, after Pope Leo III crowned Charlemagne, king of the Franks, as the "Roman Emperor" on 25 December 800, an act which eventually led to the formation of the Holy Roman Empire, the Latin West started to favour the Franks and began to refer to the Eastern Roman Empire largely as the Empire of the Greeks (Imperium Graecorum).
Document 6: Military history of France: Under Charlemagne the Franks reached the height of their power. After campaigns against Lombards, Avars, Saxons, and Basques, the resulting Carolingian Empire stretched from the Pyrenees to Central Germany, from the North Sea to the Adriatic. In 800 the Pope made Charlemagne Emperor of the West in return for protection of the Church. The Carolingian Empire was a conscious effort to recreate a central administration modeled on that of the Roman Empire,[13] but the motivations behind military expansion differed. Charlemagne hoped to provide his nobles an incentive to fight by encouraging looting on campaign. Plunder and spoils of war were stronger temptations than imperial expansion, and several regions were invaded over and over in order to bolster the coffers of Frankish nobility.[14] Cavalry dominated the battlefields, and while the high costs associated with equipping horses and horse-riders helped limit their numbers, Carolingian armies maintained an average size of 20,000 by recruiting infantry from imperial territories near theaters of operation.[15] The Empire lasted from 800 to 843, when, following Frankish tradition, it was split between the sons of Louis the Pious by the Treaty of Verdun.
Document 7: Middle Ages: Charlemagne planned to continue the Frankish tradition of dividing his kingdom between all his heirs, but was unable to do so as only one son, Louis the Pious (r. 814–840), was still alive by 813. Just before Charlemagne died in 814, he crowned Louis as his successor. Louis's reign of 26 years was marked by numerous divisions of the empire among his sons and, after 829, civil wars between various alliances of father and sons over the control of various parts of the empire. Eventually, Louis recognised his eldest son Lothair I (d. 855) as emperor and gave him Italy. Louis divided the rest of the empire between Lothair and Charles the Bald (d. 877), his youngest son. Lothair took East Francia, comprising both banks of the Rhine and eastwards, leaving Charles West Francia with the empire to the west of the Rhineland and the Alps. Louis the German (d. 876), the middle child, who had been rebellious to the last, was allowed to keep Bavaria under the suzerainty of his elder brother. The division was disputed. Pepin II of Aquitaine (d. after 864), the emperor's grandson, rebelled in a contest for Aquitaine, while Louis the German tried to annex all of East Francia. Louis the Pious died in 840, with the empire still in chaos.
Document 8: Principality of Lüneburg: The Principality of Lüneburg (later also referred to as Celle) was a territorial division of the Duchy of Brunswick-Lüneburg within the Holy Roman Empire, immediately subordinate to the emperor. It existed from 1269 until 1705 and its territory lay within the modern-day state of Lower Saxony in Germany. The principality was named after its first capital, Lüneburg (also called Lunenburg in English), which was ruled jointly by all Brunswick-Lüneburg lines until 1637. From 1378, the seat of the principality was in Celle. It lost its independence in 1705 when it was annexed by the Electorate of Brunswick-Lüneburg, but retained its vote in the Reichstag as Brunswick-Celle.
Document 9: Neumark: Called the Lubusz Land while part of medieval Poland, the territory later known as the Neumark gradually became part of the German Margraviate of Brandenburg from the mid-13th century. As Brandenburg-Küstrin the Neumark formed an independent state of the Holy Roman Empire from 1535 to 1571; after the death of the margrave John, a younger son of Joachim I Nestor, Elector of Brandenburg, it returned to Elector John George, the margrave's nephew and Joachim I Nestor's grandson. With the rest of the Electorate of Brandenburg, it became part of the Kingdom of Prussia in 1701 and part of the German Empire in 1871 when each of those states first formed. After World War I the entirely ethnic German Neumark remained within the Free State of Prussia, itself part of the Weimar Republic (Germany).
Document 10: Saxe-Lauenburg: The Duchy of Saxe-Lauenburg (, called "Niedersachsen" (Lower Saxony) between the 14th and 17th centuries), was a "reichsfrei" duchy that existed 1296–1803 and 1814–1876 in the extreme southeast region of what is now Schleswig-Holstein. Its territorial center was in the modern district of Herzogtum Lauenburg and originally its eponymous capital was Lauenburg upon Elbe, though in 1619 the capital moved to Ratzeburg.
Document 11: Holy Roman Empire: On 25 December 800, Pope Leo III crowned the Frankish king Charlemagne as Emperor, reviving the title in Western Europe, more than three centuries after the fall of the earlier ancient Western Roman Empire in 476. The title continued in the Carolingian family until 888 and from 896 to 899, after which it was contested by the rulers of Italy in a series of civil wars until the death of the last Italian claimant, Berengar I, in 924. The title was revived again in 962 when Otto I was crowned emperor, fashioning himself as the successor of Charlemagne and beginning a continuous existence of the empire for over eight centuries. Some historians refer to the coronation of Charlemagne as the origin of the empire, while others prefer the coronation of Otto I as its beginning. Scholars generally concur, however, in relating an evolution of the institutions and principles constituting the empire, describing a gradual assumption of the imperial title and role.
Document 12: Hanover: In 1636 George, Duke of Brunswick-Lüneburg, ruler of the Brunswick-Lüneburg principality of Calenberg, moved his residence to Hanover. The Dukes of Brunswick-Lüneburg were elevated by the Holy Roman Emperor to the rank of Prince-Elector in 1692, and this elevation was confirmed by the Imperial Diet in 1708. Thus the principality was upgraded to the Electorate of Brunswick-Lüneburg, colloquially known as the Electorate of Hanover after Calenberg's capital (see also: House of Hanover). Its electors would later become monarchs of Great Britain (and from 1801, of the United Kingdom of Great Britain and Ireland). The first of these was George I Louis, who acceded to the British throne in 1714. The last British monarch who ruled in Hanover was William IV. Semi-Salic law, which required succession by the male line if possible, forbade the accession of Queen Victoria in Hanover. As a male-line descendant of George I, Queen Victoria was herself a member of the House of Hanover. Her descendants, however, bore her husband's titular name of Saxe-Coburg-Gotha. Three kings of Great Britain, or the United Kingdom, were concurrently also Electoral Princes of Hanover.
Document 13: Holy Roman Empire: The Holy Roman Empire (; ) was a multi-ethnic complex of territories in Western and Central Europe that developed during the Early Middle Ages and continued until its dissolution in 1806 during the Napoleonic Wars. The largest territory of the empire after 962 was the Kingdom of Germany, though it also came to include the neighboring Kingdom of Bohemia, the Kingdom of Burgundy, the Kingdom of Italy, and numerous other territories.
Document 14: Charlemagne: Charlemagne (/ ˈʃɑːrlɪmeɪn /) or Charles the Great (2 April 742 -- 28 January 814), numbered Charles I, was King of the Franks from 768, King of the Lombards from 774 and Emperor of the Romans from 800. He united much of Europe during the early Middle Ages. He was the first recognised emperor in western Europe since the fall of the Western Roman Empire three centuries earlier. The expanded Frankish state that Charlemagne founded is called the Carolingian Empire.
Document 15: Principality of Bayreuth: The Principality of Bayreuth () or Margraviate of Brandenburg-Bayreuth ("Markgraftum Brandenburg-Bayreuth") was an immediate territory of the Holy Roman Empire, ruled by a Franconian branch of the Hohenzollern dynasty. Since Burgrave Frederick VI of Nuremberg was enfeoffed with the Margraviate of Brandenburg in 1415/17, the Hohenzollern princes transferred the margravial title to their Franconian possessions, though the principality never had been a march. Until 1604 they used Plassenburg Castle in Kulmbach as their residence, hence their territory was officially called the Principality of Kulmbach or Margraviate of Brandenburg-Kulmbach until the Empire's dissolution in 1806.
ground_truth: the Carolingian family
sub_queries: Principality of Lüneburg >> part of Answer: Holy Roman Empire
dynasty that gave birth to Holy Roman Empire Answer: the Carolingian family