Hello Diane and welcome. I don't have a dictionary in front of me here, so my definition of "hegemony" may be imprecise. I understand the word to refer to a kind of absolute power or dominance, with perhaps a connotation for the psychological or cultural aspects of power, a sort of monopoly of ideas.

For example at http://slate.msn.com/Features/NaderMS/NaderMS.asp you can read an essay by Ralph Nader titled "The Microsoft Menace
Why I'm leading a crusade to stop its drive for cyberspace hegemony."