Smooth geometry of double extension regular algebras of type (14641)

TL;DR

This paper investigates a specific class of algebraic structures called double extension regular algebras of type (14641), demonstrating that they lack differential smoothness, which impacts their geometric and algebraic properties.

Contribution

The paper establishes that double extension regular algebras of type (14641) are not differentially smooth, providing new insights into their geometric structure.

Findings

Double extension regular algebras of type (14641) are not differentially smooth.

The result impacts understanding of their geometric properties.

Provides a basis for further classification of algebraic smoothness.

Abstract

In this paper, we prove that double extension regular algebras of type (14641) are not differentially smooth.