Faithful covers of Khovanov arc algebras

TL;DR

This paper demonstrates that the extended Khovanov algebra $K^m_n$ serves as a faithful cover of the Khovanov arc algebra $H^m_n$, establishing a new algebraic relationship.

Contribution

It introduces the concept of faithfulness in covers of Khovanov arc algebras and proves the extended algebra $K^m_n$ is an $(|n-m|-1)$-faithful cover.

Findings

$K^m_n$ is an $(|n-m|-1)$-faithful cover of $H^m_n$

Establishes a new algebraic relationship between extended and standard Khovanov algebras

Provides a framework for understanding covers in Khovanov algebra theory

Abstract

We show that the extended Khovanov algebra $K^m_n$ is an $(|n-m|-1)$-faithful cover of the Khovanov arc algebra $H^m_n$.