Yes—AE-1 lenses use the Canon FD mount, and the EOS 550D uses the Canon EF/EF-S mount. Because the FD flange distance is shorter than EF, a simple mechanical adapter will not preserve infinity focus.

In practice, FD-to-EOS adapters fall into two types:

• without optics: usually only for close-up/macro use, because infinity focus is lost
• with corrective glass: can reach infinity, but often reduces image quality somewhat

Operation is fully manual: manual focus, and typically manual aperture control. There is no autofocus or normal electronic communication with the camera.

So the short answer is: yes, adapters exist, but they involve compromises. If you want convenient everyday use and full image quality, native EF/EF-S lenses are usually the better choice. If you specifically want to experiment with older manual lenses, an FD-to-EOS adapter can work with the limitations above.