We prove that for n > 2 there exists a quandle of cyclic type of size n if and only if n is a power of a prime number. This establishes a conjecture of S. Kamada, H. Tamaru and K. Wada. As a corollary, every finite quandle ...

Quandle colorings and cocycle invariants are studied for composite knots, and applied to chirality and abelian extensions. The square and granny knots, for example, can be distinguished by quandle colorings, so that a ...

We prove that rack (resp. quandle) homology of the free rack (resp. free quandle) is trivial.

We use the inflation-restriction sequence and a result of Etingof and Graña on the rack cohomology to give a explicit description of 2-cocycles of finite indecomposable quandles with values in an abelian group. Several ...

For a set theoretical solution of the Yang–Baxter equation (X, σ), we define a d.g. bialgebra B = B(X, σ), containing the semigroup algebra A = k{X}/xy = zt : σ(x, y) = (z,t) , such that k ⊗A B ⊗A k and HomA−A(B, k) are ...

This paper deals with left non-degenerate set-theoretic solutions to the Yang–Baxter equation (= LND solutions), a vast class of algebraic structures encompassing groups, racks, and cycle sets. To each such solution there ...

"El estudio de los grupos discretos de PSL(2, C) fue iniciado de manera independiente por F. Schottky, F. Klein y H. Poincare como una forma de estudiar de forma cualitativa las soluciones a ecuaciones diferenciales de ...

En este trabajo se estudia el grupo de un enlace L, es decir, el grupo fundamental del espacio S3\L, el cual es una generalización del grupo de un nudo. Esta herramienta ha sido de gran importancia a lo largo de la teoría ...

The present final master's project proposes a data tool focused on forecasting for the risk management of polypropylene prices that allows improving the decision-making processes of the hedging profile. The work is developed ...