منابع مشابه
On Finite Racks and Quandles
We revisit finite racks and quandles using a perspective based on permutations which can aid in the understanding of the structure. As a consequence we recover old results and prove new ones. We also present and analyze several examples.
متن کاملEnumerating Finite Racks, Quandles and Kei
A rack of order n is a binary operation B on a set X of cardinality n, such that right multiplication is an automorphism. More precisely, (X,B) is a rack provided that the map x 7→ x B y is a bijection for all y ∈ X, and (x B y) B z = (x B z) B (y B z) for all x, y, z ∈ X. The paper provides upper and lower bounds of the form 2cn 2 on the number of isomorphism classes of racks of order n. Simil...
متن کاملExtensions of Racks and Quandles
A rack is a set equipped with a bijective, self-right-distributive binary operation, and a quandle is a rack which satisfies an idempotency condition. In this paper, we introduce a new definition of modules over a rack or quandle, and show that this definition includes the one studied by Etingof and Graña [9] and the more general one given by Andruskiewitsch and Graña [1]. We further show that ...
متن کاملYang-Baxter deformations of quandles and racks
Given a rack Q and a ring A , one can construct a Yang-Baxter operator cQ : V ⊗ V → V ⊗ V on the free A-module V = AQ by setting cQ(x ⊗ y) = y ⊗ x y for all x, y ∈ Q . In answer to a question initiated by D.N.Yetter and P.J. Freyd, this article classifies formal deformations of cQ in the space of Yang-Baxter operators. For the trivial rack, where x = x for all x, y , one has, of course, the cla...
متن کاملOn the Orbit Decomposition of Finite Quandles
We study the structure of finite quandles in terms of subquandles. Every finite quandle Q decomposes as a union of disjoint Q-complemented subquandles which coincide with the orbits of Q. Conversely, the structure of a quandle with a given orbit decomposition is determined by rack actions satisfying a compatibility condition. We include Maple code for finding orbit decompositions and quandle st...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2006
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927870500346347