Note on the injectivity of the Loday assembly map

TL;DR

This paper demonstrates that the Loday assembly map with finite field coefficients is generally not injective for finite groups, highlighting limitations in its applicability.

Contribution

It provides the first analysis of the injectivity failure of the Loday assembly map over finite fields for finite groups.

Findings

Loday assembly map is not injective for finite groups over finite fields

Injectivity failure is a general phenomenon, not an exception

Highlights limitations in algebraic K-theory applications

Abstract

We show that for finite groups the Loday assembly map with coefficients in finite fields is in general not injective.