The 'parent' key is E Major, but it's starting on the 4th note of that key, which makes it a modal tune. The 4th mode of a parent scale (starting the Major scale on the 4th note) is a Lydian mode, so this is an A Lydian.
You've playing an E major scale, but going from A to A (A, B, C#, D#, E F#, G#, A) instead of going E to E (E, F#, G#, A, B, C#, D#, E) - same notes, different start and end points.