It seems that my livetable working like a charm now. :-)
By the way, it's a shame that boolean property didn't work
with columnsProperties with this :
#set ($columnsProperties = {
'MyBooleanPropertyField':
{"type":"list",'class':'xxxxx'},
It didn't work with text either.
Then I suppose I must change the property field type in a
database list or in static list.
Right, I found this issue for that:
http://jira.xwiki.org/browse/XWIKI-6118: "Add
boolean property support on livetables"