f-Racks, f-quandles, their extensions and cohomology
نویسندگان
چکیده
منابع مشابه
Extensions 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 کاملOn 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 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...
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We study the relationship between the Frobenius stability of an Artinian module over an F-injective ring and its stable part.
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ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2017
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s0219498817502152