Which case is "I am a professor" with identity view?
"I am a professor" is conceit not self view. But if self view arises before conceit as "professor is attā", then the conceit, which arises after that, will become misunderstood conceit.

The explanation

There are 3 clauses in tipiṭaka:


"etaṃ  mama-this is mind"  is thought by taṇhā.
"esohamasmi-I am this"  is thought by māna. &lt;&lt;&lt; this is conceit.
"eso me  attā-this is my attā" is thought by diṭṭhi. &lt;&lt;&lt; only this one is compatible with your quoted identity view,  Yamaka Sutta (SN 22.85).


But there are the complicated arising of taṇhā, māna, and diṭṭhi, because taṇhā must co-arises with only one, diṭṭhi or māna, per mind-moment arising. And  diṭṭhi can't co-arises with māna. So:

2 taṇhā = 1. sotāpanna's taṇhā 2. puthujana's taṇhā.

2 diṭṭhi = 1. sotāpanna's diṭṭhi 2. puthujana's diṭṭhi.

3 māna = 1. we are the same 2. I am better 3. I am worse.


There are sotāpanna's taṇhā and 3 māna of sotāpanna, but there are not diṭṭhi of sotāpanna.
There are 2 taṇhā, 9 māna, and 2 diṭṭhi of puthujana.


Therefore, there are just 3 māna of sotāpanna, but there are 9 māna for puthujana, 6 Diṭṭhi-Before&amp;After(misunderstood) and 3 No-Diṭṭhi-Before&amp;After māna's arising (right understood).


  
  "eso me  attā-this is my attā" is thought by diṭṭhi. &lt;&lt;&lt; only this one is compatible with your quote,  Yamaka Sutta (SN 22.85).
  


There are 20 sakkāya-diṭṭhi which thinking about attā in Yamaka Sutta (SN 22.85).