On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size. Issue 5 (3rd May 2020)

• Record Type: Journal Article
• Authors: Castelli, M.; Pinto, G.; Rump, W.
• Is Part Of: Communications in algebra. Volume 48:Issue 5(2020)
• Page Start: 1941
• Page End: 1955
• Publication Date: 2020-05-03
• Subjects: Cycle set -- set-theoretic solution -- Yang-Baxter equation; 16T25 -- 20E22 -- 20F16; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1710163
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: We develop a method to construct all the indecomposable involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation with a prime-power number of elements and cyclic permutation group. Moreover, we give a complete classification of the indecomposable ones having abelian permutation group and cardinality pq (where p and q are prime numbers not necessarily distinct).