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- W4300802600 abstract "While homology theory of associative structures, such as groups and rings, has been extensively studied in the past beginning with the work of Hopf, Eilenberg, and Hochschild, homology of non-associative distributive structures, such as quandles, were neglected until recently. Distributive structures have been studied for a long time. In 1880, C.S. Peirce emphasized the importance of (right) self-distributivity in algebraic structures. However, homology for these universal algebras was introduced only sixteen years ago by Fenn, Rourke, and Sanderson. We develop this theory in the historical context and propose a general framework to study homology of distributive structures. We illustrate the theory by computing some examples of 1-term, 2-term, and 3-term homology, and then discussing 4-term homology for Boolean algebras and distributive lattices. We outline potential relations to Khovanov homology, via the Yang-Baxter operator." @default.
- W4300802600 created "2022-10-04" @default.
- W4300802600 creator A5074798942 @default.
- W4300802600 date "2011-09-22" @default.
- W4300802600 modified "2023-09-24" @default.
- W4300802600 title "Distributivity versus associativity in the homology theory of algebraic structures" @default.
- W4300802600 doi "https://doi.org/10.48550/arxiv.1109.4850" @default.
- W4300802600 hasPublicationYear "2011" @default.
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