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The Inca Empire was centered in what is now Peru from AD 1438 to AD 1533. This civilization is renowned for its advanced architecture, agricultural practices, and extensive road systems. The Incas developed a sophisticated society that included a centralized government led by an emperor, advanced agricultural terraces, and significant contributions to art and engineering. Their capital city, Cusco, was a hub of political, cultural, and religious activities, indicating the empire's wealth and organization.

In contrast, the Mayas flourished in present-day Mexico and Central America, notable for their accomplishments in writing, astronomy, and mathematics but not in the region of Peru. The Aztecs were primarily located in what is now central Mexico, famous for their vast empire and complex societal structure, while the Olmecs were one of the earliest known Mesoamerican civilizations, also distinct from the Andean geography of the Incas. Thus, the Inca Empire is correctly identified as the empire central to Peru during that specific historical timeframe.