# Higher Spherical Algebras

## TL;DR

This paper introduces higher spherical algebras, a new class of finite-dimensional algebras, and proves their derived equivalence to higher tetrahedral algebras, establishing their tameness, symmetry, and periodicity.

## Contribution

It defines higher spherical algebras and shows they are derived equivalent to known higher tetrahedral algebras, revealing their tame symmetric periodic nature.

## Key findings

- Higher spherical algebras are derived equivalent to higher tetrahedral algebras.
- They are tame symmetric periodic algebras of period four.
- The study expands understanding of algebra classifications and derived equivalences.

## Abstract

We introduce and study higher spherical algebras, an exotic family of finite-dimensional algebras over an algebraically closed field. We prove that every such an algebra is derived equivalent to a higher tetrahedral algebra studied in [7], an hence that it is a tame symmetric periodic algebra of period four.