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Link and knot invariants from non-abelian Yang-Baxter 2-cocycles
(World Scientific, 2016-11)
We define a knot/link invariant using set theoretical solutions (X,σ) of the Yang-Baxter equation and non-commutative 2-cocycles. We also define, for a given (X,σ), a universal group Unc(X) governing all 2-cocycles in X, ...
Standard cocycles: Variations on themes of C. Kassel's and R. Wilson's
(De Gruyter, 2017-11)
Central extensions of Lie algebras can be understood and classified by means of 2-cocycles. The Lie algebras we are interested in are "twisted forms" (defined by Galois descent) of algebras of the form g⊗ kR with g split ...
Analiticity of the Lyapunov exponents of random products of quasi-periodic cocycles
(2021-11-01)
We show that the top Lyapunov exponent LE(p) associated with a random product of quasi-periodic cocycles depends real analytically on the transition probabilities p whenever LE(p) is simple. Moreover if the spectrum at ...
Deformation by cocycles of pointed Hopf algebras over non-abelian groups
(International Press Boston, 2015-01)
We explore a method for explicitly constructing multiplicative 2-cocycles for bosonizations of Nichols algebras B(V ) over Hopf algebras H. These cocycles arise as liftings of H-invariant linear functionals on V⊗ V and ...
Quandle coloring and cocycle invariants of composite knots and abelian extensions
(World Scientific, 2016-04)
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 ...
Link and knot invariants from non-abelian Yang–Baxter 2-cocycles
(World Scientific, 2016-11)
We define a knot/link invariant using set theoretical solutions (X, σ) of the Yang-Baxter equation and non commutative 2-cocycles. We also define, for a given (X, σ), a universal group Unc(X) governing all 2-cocycles in ...