# Linear Preserver Problems and Algebraic Groups

## Document Type

Presentation Abstract

## Presentation Date

11-25-2013

## Abstract

In 1897 Frobenius posed and solved the following problem: Determine the set of all endomorphisms of the space of complex n by n matrices that preserve the values of the determinant. This is the first example of a Linear Preserver Problem. The work I will discuss in this talk began with an attempt to find a solution to an interesting class of such problems. Our methods of attack come from the theory of Linear Algebraic Groups; I will give an overview of the basic concepts and then apply them to describe the solution of some LPP's. In an interesting recent development it turns out that understanding the solution of the LPP's in turn gives a great deal of information about the general structure of Linear Algebraic Groups.

## Recommended Citation

Bermudez, Hernando, "Linear Preserver Problems and Algebraic Groups" (2013). *Colloquia of the Department of Mathematical Sciences*. 440.

https://scholarworks.umt.edu/mathcolloquia/440

## Additional Details

Monday, November 25 at 3:10 p.m. in Math 103