I have this use case: I want to apply a dimension reduction with UMAP to a initial dataset of high-dimension vectors (100d), and later, in second place, have the oppurtinity to add new data points from the original space (so a vector of 100d), that will be transformed according to the first transformation (aka without recalculating the umap vectors for the first N vectors). Is it possible? Does UMAP have a transformation matrix ( or similar)?
UMAP has a transform method that can achieve this. Note that this is a somewhat expensive computation, and not almost instant as it can be with, for example, PCA. See the UMAP documentation for more details.
If you need a very fast transform method for new data then I would encourage you to look at Parametric UMAP which uses a neural network to learn a direct mapping from input space to the embedding space and provides very efficient transforms.