aperture

. I imported my library (from an other computer)

How did you import the library? If you did not import the library using "File > Import > Library" you will not have migrated the albums and products.

Try to open the library instead. Copy the original library to your new computer and double-click it to open it in Aperture and to upgrade the library to anew format.

So I import the library from another computer (I connected the two computers en shared all my files).

Is it a wired connection (Firewire, Thunderbolt) or a network connection?

but the albums are empty

Do you see the albums, but they are empty? Are are the albums missing altogether?

Aperture libraries (and iPhoto Libraries) are not supported on network volumes. Accessing the library this way may cause library corruption and data loss, be careful, see this link:

Use locally mounted Mac OS X Extended volumes for your Aperture library

and also:

iPhoto: Sharing libraries among multiple users

If you don't have enough space on your new mac, copy the library to an extern drive, formatted as described in the second link above.

Your library has probably a permissions or access control list problem, since it has been created using a different user account. After moving the library to a different drive run a permissions repair. I'd not do that, while the library is still on the network volume.

To repair the permissions launch Aperture with options-command keys held down, until you are seeing the first aid panel, and select "Repair permissions".