Title: On Lie isomorphisms of rings
Speaker: Iryna Kashuba（Southern University of Science and Technology）
Time: 9.19 (Friday), 15:00-16:00
Venue: Gewu Building 315
Abstract ：An associative ring A gives rise to the Lie ring A^{(−)} = (A, [a, b] = ab − ba). We prove that if the identity element of A decomposes into a sum of at least three full orthogonal idempotents, then any isomorphism from the Lie ring [A, A] to the Lie ring [B, B] is standard. We also discuss a version for non-unital A and then apply it to the describe automorphisms and derivations of Lie algebras of infinite matrices. We also apply this technique to the case of infinite polinomials. This is joint work with O. Bezushchak and E. Zelmanov.
