Question: Sigtrygg II Silkbeard Olafsson, was a Hiberno-Norse king of which location, of the Uí Ímair dynasty?

Context articles: Uí Ímair
Ímar
Cogad Gáedel re Gallaib
Battle of Mag Femen
Máel Muire ingen Amlaíb
Amlaíb mac Sitriuc
Amlaíb Conung
Battle of Islandbridge
Sigtrygg Silkbeard
Sitric Cáech

The Uí (h)Ímair ] , or Dynasty of Ivar, was a royal Norse dynasty which ruled much of the Irish Sea region, the Kingdom of Dublin, the western coast of Scotland, including the Hebrides and some part of Northern England, from the mid 9th century.
Ímar (Old Norse: "Ívarr" ; died c. 873) was a Viking leader in Ireland and Scotland in the mid-late ninth century who founded the Uí Ímair dynasty, and whose descendants would go on to dominate the Irish Sea region for several centuries.
 He was the son of the king of Lochlann, identified in the non-contemporary "Fragmentary Annals of Ireland" as Gofraid.
 The "Fragmentary Annals" name Auisle and Amlaíb Conung as his brothers.
 Another Viking leader, Halfdan Ragnarsson, is considered by some scholars to be another brother.
 The Irish Annals title Amlaíb, Ímar and Auisle "kings of the foreigners".
 Modern scholars use the title "kings of Dublin" after the Viking settlement which formed the base of their power.
 Some scholars consider Ímar to be identical to Ivar the Boneless, a Viking commander of the Great Heathen Army named in contemporary English sources who also appears in the Icelandic sagas as a son of the legendary Viking Ragnar Lodbrok.
Cogad Gáedel re Gallaib ("The War of the Irish with the Foreigners") is a medieval Irish text that tells of the depredations of the Vikings and Uí Ímair dynasty in Ireland and the Irish king Brian Boru's great war against them, beginning with the Battle of Sulcoit in 967 and culminating in the Battle of Clontarf in 1014, in which Brian was slain but his forces were victorious.
 The chronicle, which compares King Brian to Augustus and Alexander the Great, was written in the early twelfth century, at least a hundred years after the events it describes.
 Much of the narrative is drawn from the earlier Annals of Ulster.
The Battle of Mag Femen took place on 22 August 917 between the Vikings of the Uí Ímair, led by Ragnall, a grandson of Ímar, and the Irish of the Northern Uí Néill, led by Niall Glúndub, High King of Ireland.
 It was one of two battles involving the Uí Ímair that year, the other being the Battle of Confey, which occurred as a result of the Uí Ímair trying to retake the Kingdom of Dublin which they had lost in 902.
 The battle began when Niall Glúndub's forces attacked a Viking army at a site identified by the annals as Topar Glethrach in Mag Femen.
 The Irish initially inflicted the majority of the casualties, but late in the day a host of more troops led by Ragnall reinforced the Viking army, securing the victory for the Uí Ímair.
Máel Muire (died 1021) was Queen of Ireland, being actually styled so in the Annals of Clonmacnoise.
 The wife of Máel Sechnaill mac Domnaill, High King of Ireland, she was a daughter of Amlaíb Cuarán, King of Dublin until 980/1 and formerly King of York.
 Thus she was a member of the Norse-Irish Uí Ímair dynasty and the first Queen of Ireland of ultimately foreign or non-Celtic lineage known to be historical.
 One of her brothers was the celebrated King of Dublin Sitric Silkbeard, while a sister Gytha was wife to Olaf Tryggvason, King of Norway.
Amlaíb mac Sitriuc ("Amhlaeibh, son of Sitric") or Olaf Sigtryggsson was the son of Sigtrygg Silkbeard, the Hiberno-Norse King of Dublin, and Sláine, the daughter of Brian Boru.
 A member of the Uí Ímair dynasty, his ancestors also included Amlaíb Cuarán and Gormflaith, who were influential in medieval Ireland.
 He was ransomed by the Gaelic lord of Brega and later killed in England by Anglo-Saxons while on his way on pilgrimage to Rome in 1034.
 Some of his descendants later became the Kings of Gwynedd in Wales.
Amlaíb Conung (Old Norse: "Óláfr" ; died c. 874) was a Viking leader in Ireland and Scotland in the mid-late ninth century.
 He was the son of the king of Lochlann, identified in the non-contemporary "Fragmentary Annals of Ireland" as Gofraid, and brother of Auisle and Ímar, the latter of whom founded the Uí Ímair dynasty, and whose descendants would go on to dominate the Irish Sea region for several centuries.
 Another Viking leader, Halfdan Ragnarsson, is considered by some scholars to be another brother.
 The Irish Annals title Amlaíb, Ímar and Auisle "kings of the foreigners".
 Modern scholars use the title "kings of Dublin" after the Viking settlement which formed the base of their power.
 The epithet "Conung" is derived from the Old Norse "konungr" and simply means "king".
 Some scholars consider Amlaíb to be identical to Olaf the White, a Viking sea-king who features in the "Landnámabók" and other Icelandic sagas.
The Battle of Islandbridge, also called the Battle of Áth Cliath, took place on 14 September 919, between a coalition of native Irish, led by Niall Glúndub, overking of the Northern Uí Néill and High King of Ireland, and the Dublin-based Vikings of the Uí Ímair, led by Sitric Cáech.
 It was one in a series of battles initiated by the native Irish to attempt to drive the Vikings of the Uí Ímair from Ireland.
 The battle was a decisive victory for Sitric Cáech and the Uí Ímair, with Niall Glúndub and five other Irish kings dying in the battle.
Sigtrygg II Silkbeard Olafsson (also Sihtric, Sitric and Sitrick in Irish texts; or Sigtryg and Sigtryggr in Scandinavian texts) was a Hiberno-Norse king of Dublin (possibly AD 989–994; restored or began 995–1000; restored 1000 and abdicated 1036) of the Uí Ímair dynasty.
 He was caught up in the abortive Leinster revolt of 999–1000, after which he was forced to submit to the King of Munster, Brian Boru.
 His family also conducted a double marriage alliance with Boru, although he later realigned himself with the main leaders of the Leinster revolt of 1012–1014.
 He has a prominent role in the 12th-century Irish "Cogadh Gaedhil re Gallaibh" and the 13th century Icelandic "Njal's Saga", as the main Norse leader at the Battle of Clontarf in 1014.
Sitric Cáech, also known as Sitric Gále, (Old Norse: "Sigtryggr" , died 927) was a Viking leader who ruled Dublin and then Viking Northumbria in the early 10th century.
 He was a grandson of Ímar and a member of the Uí Ímair.
 Sitric was most probably among those Vikings expelled from Dublin in 902, whereafter he may have ruled territory in the eastern Danelaw in England.
 In 917, he and his kinsman Ragnall ua Ímair sailed separate fleets to Ireland where they won several battles against local kings.
 Sitric successfully recaptured Dublin and established himself as king, while Ragnall returned to England to become King of Northumbria.
 In 919, Sitric won a victory at the Battle of Islandbridge over a coalition of local Irish kings who aimed to expel the Uí Ímair from Ireland.
 Six Irish kings were killed in the battle, including Niall Glúndub, overking of the Northern Uí Néill and High King of Ireland.