The j is often used in combination with another vowel to make a dipthong. For instance, ja ~ Я
Now, these "hard vowels" or dipthings will palatalize a preciding "soft consonant".
So I presume Ljubljana (you have one i too many, BTW) would be transcribed as Любляна and the L's are pronounced palatalised as lj (the same sound as Spanish ll, Italian gli, or or French ill). We have met the enemy, and he is us — Pogo
And Я isn't a diphtong ; in isolation it represent yod+a ; after a consonant it represents a soft consonant (except after ь or ъ). From my russian phonetics courses the 'hard vowels' actually indicate a phonetically different consonant, and it is a bit wrong to think that the vowel modifies the consonant ; consonants are inherently 'soft', or 'hard', and modify the way the vowel is pronounced and written. Un roi sans divertissement est un homme plein de misères
The cyrillic transcription is correct, though.
Certain consonants such as l are ambiguous in that they take both hard and soft vowels and their pronunciation changes accordingly.
The phoneme to grapheme mapping is far from perfect in this case. We have met the enemy, and he is us — Pogo
Ya (Я, я) is a letter in the Cyrillic alphabet, representing either the combination ja (a so-called iotated vowel) or a after a palatalized consonant.
This must be a huge headache for Western students of Slavic languages who don't know anything about phonology. We have met the enemy, and he is us — Pogo