# Mathematics Algebra Seminar - Bakhyt Aitzhanova

This event is in the past.

**Date:**November 1, 2022

**Time:**1:00 p.m. - 2:00 p.m.

**Category:**Seminar

**Speaker:** Bakhyt Aitzhanova, Wayne State University

**Title:** Automorphisms of affine Veronese surfaces

**Abstract:** We prove that every derivation and every locally nilpotent derivation of the subalgebra $K[x^n, x^{n-1}y,ldots,xy^{n-1}, y^n]$, where $ngeq 2$, of the polynomial algebra $K[x,y]$ in two variables over a field $K$ of characteristic zero is induced by a derivation and a locally nilpotent derivation of $K[x,y]$, respectively. Moreover, we prove that every automorphism of $K[x^n, x^{n-1}y,ldots,xy^{n-1}, y^n]$ over an algebraically closed field $K$ of characteristic zero is induced by an automorphism of $K[x,y]$. We also show that the group of automorphisms of $K[x^n, x^{n-1}y,ldots,xy^{n-1}, y^n]$ admits an amalgamated free product structure.

## Contact

Department of Mathematics

313-577-2479

math@wayne.edu