There are two-way prepositions that can be either accusative or dative. If the preposition in the sentence answers the question "where to?" (meaning the object in question is at work at reaching its destination) it is accusative. If the sentence answers the question "where?" (meaning the object in question is already at that place) it is dative. In this case, the "best wishes" are directed "to" your mother, so as it implies motion, it's accusative.
I suspect it's because 'an' translates to 'to' rather than 'on' in this situation; however, I can't find the answer elsewhere. Edit: Nope, I'm wrong. It is something to do with motion.
You're kinda right though, 'to' would only be used for movement, and 'on' only for location. So it's fair to say that when 'an' translates to 'to', it takes accusative, and for 'on' it takes dative. (Although if it translates as 'onto', it's movement, so it's accusative). This is only for two-way prepositions though, 'zu' can mean 'to' as well, but it isn't two-way, and it always takes the dative.
But I'm pretty sure when it comes to physical locations and directions "on" translates to auf with dative and accusative respectively.
Ah very true. Because the painting isn't actually atop the wall, but attached to it.
Yeah, the way I understand it the 'greetings' are being sent, hence it is considered a motion. :P
Viele Grüße = many greetings, regards. Best wishes = gute Wünsche, alles Gute
if i would want to tell "to" when i have to use an, zu, für, um, bei, or mit.
"Best wishes ...." is good, but kind of formal. Simply "Greetings to .." is much better, but probably not accepted without the adjective.
Could anybody explain why after 'an', that is a two-ways preposition, and there is no movement involved, there is the Accusative instead of Dative case?
You could think of it as similar to:
- As-salamu alaykum
- Pax vobis
- Shalom aleichem
all of which roughly translate to "Peace be upon you."
But just like mizinamo said: prepositions do not translate easily and are highly context-dependent.