Dual alternative algebras in characteristic three

TL;DR

This paper determines the dimension of the arity n component of the operad of dual alternative algebras over a field of characteristic three and describes its symmetric group module structure.

Contribution

It provides the exact dimension formula and module structure for dual alternative operads in characteristic three, a previously uncharacterized case.

Findings

Dimension of arity n component is 2^n - n in characteristic three.

Describes the S_n-module structure of the operad.

Advances understanding of dual alternative operads in characteristic three.

Abstract

We prove that the dimension of the arity $n$ component of the operad of dual alternative algebras over a field of characteristic three is equal to $2^n-n$, and describe the structure of the corresponding $S_n$-module.