Homology theory for the set-theoretic Yang–Baxter equation and knot invariants from generalizations of quandles
By J. Scott Carter, Mohamed Elhamdadi, Masahico Saito. 2002
143 citations recorded by the source corpus.
A homology theory is developed for set-theoretic Yang-Baxter equations, and knot invariants are constructed by generalized colorings by biquandles and Yang-Baxter cocycles.
View Paper: https://www.semanticscholar.org/paper/349eb9d02f871cedf641b934e60f3aa5afd22cdb
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Citations in the corpus
- Homology of left non-degenerate set-theoretic solutions to the Yang–Baxter equation (2015, methodology): “–Jelsovsky–Kamada–Langford–Saito [6], and further developed by Andruskiewitsch–Gran˜a [1]. Rack (co)homology theories were generalized to the case of arbitrary braided sets by Carter– Elhamdadi–Saito [5] and further developed by the first author [26]. For biracks, Fenn, Rourke, and Sanderson [19] con”
- Matrices and finite biquandles (2006, methodology): “The resulting algebraic structure is called a biquandle; see [2], [6], [4], and [12], for example.”
- Cohomology of Categorical Self-Distributivity (2006, unknown): “Generalizations have been discovered [1, 8, 9].”