Journal of Homotopy and Related Structures

, Volume 12, Issue 3, pp 741–763 | Cite as

On homology of associative shelves

  • Alissa S. Crans
  • Sujoy Mukherjee
  • Józef H. PrzytyckiEmail author


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.


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

Mathematics Subject Classification

Primary 18G60 Secondary 20M32 20N02 57M25 



The authors would like to thank Maciej Niebrzydowski for initial computations and Marithania Silvero for useful comments and suggestions. Furthermore, the authors would like to thank the referee for comments and suggestions.


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Copyright information

© Tbilisi Centre for Mathematical Sciences 2016

Authors and Affiliations

  • Alissa S. Crans
    • 1
  • Sujoy Mukherjee
    • 2
  • Józef H. Przytycki
    • 2
    • 3
    Email author
  1. 1.Department of MathematicsLoyola Marymount UniversityLos AngelesUSA
  2. 2.Department of MathematicsThe George Washington UniversityWashington DCUSA
  3. 3.University of GdańskGdańskPoland

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