The VEGAS imaging survey of the Hydra I cluster reveals an extended network of stellar filaments to the south-west of the spiral galaxy NGC3314A. Within these filaments, at a projected distance of ~40 kpc from the galaxy, we discover an ultra-diffuse galaxy (UDG) with a central surface brightness of $mu_{0,g}sim26$ mag arcsec$^{-2}$ and effective radius $R_esim3.8$ kpc. This UDG, named UDG32, is one of the faintest and most diffuse low-surface brightness galaxies in the Hydra~I cluster. Based on the available data, we cannot exclude that this object is just seen in projection on top of the stellar filaments, thus being instead a foreground or background UDG in the cluster. However, the clear spatial coincidence of UDG32 with the stellar filaments of NGC3314A suggests that it might have formed from the material in the filaments, becoming a detached, gravitationally bound system. In this scenario, the origin of UDG32 depends on the nature of the stellar filaments in NGC3314A, which is still unknown. They could result from ram-pressure stripping or have a tidal origin. In this letter, we focus on the comparison of the observed properties of the stellar filaments and UDG32, and speculate about their possible origin. The relatively red color ($g-r=0.54 pm 0.14$~mag) of the UDG, similar to that of the disk in NGC3314A, combined with an age older than 1Gyr, and the possible presence of a few compact stellar systems, all point towards a tidal formation scenario inferred for the UDG32.
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