Context: Narrow-band surveys for Ly-alpha emitters (LAEs) is a powerful tool in detecting high, and very high, redshift galaxies. Even though samples are growing at redshifts z = 3 - 6, the nature of these galaxies is still poorly known. Aims: To study the properties of z = 2.25 LAEs and compare those with the properties of z > 3 LAEs. Methods: We present narrow-band imaging made with the MPG/ESO 2.2m telescope with the WFI detector. We have made a selection for emission-line objects and find 170 candidate typical LAEs and 17 candidates which we regard as high UV-transmission LAEs. We have derived the magnitudes of these objects in 8 bands from u* to Ks, and studied if they have X-ray and/or radio counterparts. Results: We show that there has been significant evolution in the properties of LAEs between redshift z ~ 3 and z = 2.25. The spread in spectral energy distributions (SEDs) at the lower redshift is larger and we detect a significant AGN contribution in the sample. The distribution of the equivalent widths is narrower than at z ~ 3, with only a few candidates with rest-frame equivalent width above the predicted limit of 240 A. The star formation rates derived from the Ly-alpha emission compared to that derived from the UV emission are lower by on average a factor of ~ 1.8, indicating a large absorption of dust. Conclusion: LAEs at redshift z = 2.25 may be more evolved than LAEs at higher redshift. The red SEDs imply more massive, older and/or more dusty galaxies at lower redshift than observed at higher redshifts. The decrease in equivalent widths and star formation rates indicate more quiescent galaxies, with in general less star formation than in higher redshift galaxies. At z = 2.25, AGN appear to be more abundant and also to contribute more to the LAE population. [Abridged]
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