# Schur Multipliers and Second Quandle Homology

## TL;DR

This paper explores the relationship between second quandle homology and the Schur multiplier, providing new theoretical insights and computational examples for Alexander quandles.

## Contribution

It introduces a map from second quandle homology to the Schur multiplier and expresses Alexander quandle homology via exterior algebras, with a self-contained proof.

## Key findings

- Established a map linking second quandle homology to the Schur multiplier
- Expressed Alexander quandle homology in terms of exterior algebras
- Provided computational examples and a complete proof of the structure

## Abstract

We define a map from second quandle homology to the Schur multiplier and examine its properties. Furthermore, we express the second homology of Alexander quandles in terms of exterior algebras. Additionally, we present a self-contained proof of its structure and provide some computational examples.