# On the representation dimension and finitistic dimension of special multiserial algebras

## TL;DR

This paper proves that all special multiserial algebras have a representation dimension at most three, confirming the finitistic dimension conjecture for this class by constructing radical embeddings into finite type algebras.

## Contribution

It establishes a bound on the representation dimension of monomial and self-injective special multiserial algebras and confirms the finitistic dimension conjecture for all special multiserial algebras.

## Key findings

- Representation dimension ≤ 3 for monomial and self-injective special multiserial algebras
- Construction of radical embeddings into finite representation type algebras
- Finitistic dimension conjecture holds for all special multiserial algebras

## Abstract

For monomial special multiserial algebras, which in general are of wild representation type, we construct radical embeddings into algebras of finite representation type. As a consequence, we show that the representation dimension of monomial and self-injective special multiserial algebras is less or equal to three. This implies that the finitistic dimension conjecture holds for all special multiserial algebras.