Two-sided vector spaces

TL;DR

This paper characterizes simple two-sided vector spaces over perfect fields, computes their Quillen K-theory, and explores related homomorphism structures, advancing understanding of their algebraic and categorical properties.

Contribution

It provides a complete classification of simple two-sided vector spaces over perfect fields and calculates their Quillen K-theory, linking algebraic structures with K-theoretic invariants.

Findings

Complete classification of simple two-sided vector spaces

Calculation of Quillen K-theory for these categories

Description of homomorphisms from fields to matrix rings

Abstract

We study the structure of two-sided vector spaces over a perfect field $K$. In particular, we give a complete characterization of isomorphism classes of simple two-sided vector spaces which are left finite-dimensional. Using this description, we compute the Quillen $K$-theory of the category of left finite-dimensional, two-sided vector spaces over $K$. We also consider the closely related problem of describing homomorphisms $\phi:K\to M_n(K)$.