Homology of Associative Shelves

TL;DR

This paper explores homology theories for associative self-distributive algebraic structures, focusing on their one-term and rack homology groups, bridging classical associative algebra and knot-theoretic structures.

Contribution

It introduces and investigates homology groups for associative self-distributive structures, connecting associative algebra with knot theory concepts.

Findings

Analysis of one-term homology groups

Investigation of rack homology groups

Establishment of foundational properties

Abstract

Homology theories for associative algebraic structures are well established and have been studied for a long time. More recently, homology theories for self-distributive algebraic structures motivated by knot theory, such as quandles and their relatives, have been developed and investigated. In this paper, we study associative self-distributive algebraic structures and their one-term and two-term (rack) homology groups.