Braided Symmetric and Exterior Algebras

TL;DR

This paper explores the construction and properties of symmetric and exterior algebras within braided monoidal categories, particularly focusing on quantum groups, and compares them to classical algebraic structures.

Contribution

It introduces braided symmetric and exterior algebras in the context of quantum groups and relates them to classical algebraic structures.

Findings

Braided symmetric and exterior algebras are constructed in quantum group categories.

Connections between braided and classical symmetric and exterior algebras are established.

The study enhances understanding of algebraic structures in braided monoidal categories.

Abstract

We introduce and study symmetric and exterior algebras in braided monoidal categories such as the category O for quantum groups. We relate our braided symmetric algebras and braided exterior algebas with their classical counterparts.