On Homology of Associative Shelves

Alissa S. Crans; Sujoy Mukherjee; Jozef H. Przytycki

doi:10.1007/s40062-016-0164-9

On Homology of Associative Shelves

Alissa S. Crans, Sujoy Mukherjee, Jozef H. Przytycki

Mathematics, Statistics and Data Science

Research output: Contribution to journal › Article › peer-review

Abstract

Homology theories for associative algebraic structures are well established and have been studied for a long time. More recently, homology theories for selfdistributive 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.

Original language	English
Pages (from-to)	741-763
Number of pages	23
Journal	Journal of Homotopy and Related Structures
Volume	12
Issue number	3
DOIs	https://doi.org/10.1007/s40062-016-0164-9
State	Published - Sep 2017

Keywords

Knot theory
Laver tables
One-term and two-term (rack) distributive homology
Self-distributive semigroups
Spindles
Unital

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10.1007/s40062-016-0164-9License: Unspecified

http://digitalcommons.lmu.edu/math_fac/176

Cite this

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title = "On Homology of Associative Shelves",

abstract = "Homology theories for associative algebraic structures are well established and have been studied for a long time. More recently, homology theories for selfdistributive 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.",

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KW - Knot theory

KW - Laver tables

KW - One-term and two-term (rack) distributive homology

KW - Self-distributive semigroups

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KW - Unital

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