Catalyzes the transfer of an amino group between 2-oxoadipate (2-OA) and glutamate (Glu) to yield alpha-aminodipate (AAA). It can also transaminate glutamate, leucine, and aromatic amino acids. It also contributes in the biosynthesis of other amino acids such as leucine. 2-oxoglutarate + L-2-aminoadipate = 2-oxoadipate + L-glutamate Amino-acid biosynthesis; L-lysine biosynthesis via AAA pathway; L-alpha-aminoadipate from 2-oxoglutarate: step 5/5. Homodimer. Catalysis proceeds by a classical ping-pong bi-bi reaction mechanism. Belongs to the class-I pyridoxal-phosphate-dependent aminotransferase family.