Quadratic maps between groups

TL;DR

This paper provides a comprehensive study of quadratic maps between groups, exploring their properties, relationships with polynomial maps, and implications for groups of degree 2, thereby unifying various concepts in quadratic algebra.

Contribution

It offers a unified, extensive treatment of quadratic maps between groups and connects them with polynomial maps and groups of degree 2, advancing theoretical understanding.

Findings

Established the relation between quadratic maps and Passi's polynomial maps.

Analyzed the structure of groups of degree 2 using quadratic maps.

Unified various existing notions of quadratic algebra in a comprehensive framework.

Abstract

The notion of quadratic maps between arbitrary groups appeared at several places in the literature on quadratic algebra. Here a unified extensive treatment of their properties is given; the relation with a relative version of Passi's polynomial maps and groups of degree 2 is established and used to study the structure of the latter.