Nichols algebras of U_q(g)-modules

TL;DR

This paper introduces a method to analyze Nichols algebras of U_q(g)-modules by reducing the problem to braided vector spaces, providing new insights into their dimensions and relations, especially for simple g.

Contribution

The paper develops a technique to simplify the study of Nichols algebras of U_q(g)-modules by focusing on diagonal braiding cases, advancing understanding of their structure and dimensions.

Findings

Determined cases of finite Gelfand-Kirillov dimension for simple g.

Provided relations for Nichols algebras with special braiding types.

Analyzed the dimensions of Nichols algebras when q is not a root of unity.

Abstract

A technique is developed to reduce the investigation of Nichols algebras of integrable U_q(g)-modules to the investigation of Nichols algebras of braided vector spaces with diagonal braiding. The results are applied to obtain information on the Gelfan'd-Kirillov dimension of these Nichols algebras and their defining relations if the braiding is of a special type and q is not a root of unity. For simple g the cases of finite Gelfand-Kirillov dimension are determined completely.