# Two-Sided Vector Spaces

## Document Type

Presentation Abstract

## Presentation Date

4-4-2003

## Abstract

A two-sided vector space over a field K is a set V and a pair of actions of K on V, *(x,v)* ι→ xv and *(v,x)* ι→ *vx*, such that each action individually makes V into a vector space over K, satisfying an associativity condition.

Every ordinary vector space is a two-sided vector space, but there are interesting examples where the left and right actions do not agree. Motivated by some problems in "noncommutative algebraic geometry," we look at the structure of two-sided vector spaces in some detail. The results end up depending on the arithmetic of the field K. The problem can be formulated purely in terms of linear algebra. (This work is joint with A. Nyman at the University of Montana.)

## Recommended Citation

Pappacena, Dr. Christopher J., "Two-Sided Vector Spaces" (2003). *Colloquia of the Department of Mathematical Sciences*. 137.

https://scholarworks.umt.edu/mathcolloquia/137

## Additional Details

Friday, 4 April 2003

4:10 p.m. in Math 109

Coffee/treats at 3:30 p.m. Math 104 (Lounge)