# Homological dimensions of smooth crossed products

## TL;DR

This paper estimates the global projective dimensions of smooth crossed products involving certain groups and algebras, extending existing methods to new classes of algebras.

## Contribution

It introduces a generalized method for estimating homological dimensions of smooth crossed products with specific groups and algebras.

## Key findings

- Upper bounds for global projective dimensions of smooth crossed products.
- Extension of methods used in previous works to broader algebra classes.
- Application to groups G = R and G = T.

## Abstract

In this paper we provide upper estimates for the global projective dimensions of smooth crossed products $\mathscr{S}(G, A; \alpha)$ for $G = \mathbb{R}$ and $G = \mathbb{T}$ and a self-induced Fr\'echet-Arens-Michael algebra $A$. In order to do this, we provide a powerful generalization of methods which are used in the works of Ogneva and Helemskii.