Cocycle Twists of Algebras
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Cocycle Deformations for Hopf Algebras with a Coalgebra Projection
In this paper we study Hopf algebras with a coalgebra projection A ∼= R#ξH and their deformations by an H-bilinear cocycle. If γ is a cocycle for A, then γ can be restricted to a cocycle γR for R, and A γ ∼= RR#ξγH. As examples, we consider liftings of B(V )#K[Γ] where Γ is a finite abelian group, V is a quantum plane and B(V ) is its Nichols algebra, and explicitly construct the cocycle which ...
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We give an explicit formula for the correspondence between simple Yetter-Drinfeld modules for certain finite-dimensional pointed Hopf algebras H and those for cocycle twists H of H. This implies an equivalence between modules for their Drinfeld doubles. To illustrate our results, we consider the restricted two-parameter quantum groups ur,s(sln) under conditions on the parameters guaranteeing th...
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Let H be a Hopf algebra with bijective antipode over a field k and suppose that R#H is a bi-product. Then R is a bialgebra in the Yetter–Drinfel’d category HYD. We describe the bialgebras (R#H) and (R#H) explicitly as bi-products R#Hop and R#H respectively where R is a bialgebra in H op HopYD and R o is a bialgebra in H o HoYD. We use our results to describe two-cocycle twist bialgebra structur...
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Let $mathcal{R}$ be a commutative ring with identity, let $A$ and $B$ be two $mathcal{R}$-algebras and $varphi:Blongrightarrow A$ be an $mathcal{R}$-additive algebra homomorphism. We introduce a new algebra $Atimes_varphi B$, and give some basic properties of this algebra. Generalized $2$-cocycle derivations on $Atimes_varphi B$ are studied. Accordingly, $Atimes_varphi B$ is considered from th...
متن کاملExtensions of Peripheric Extended Twists and Inhomogeneous Lie Algebras
Simple extensions of peripheric extended twists, introduced recently by Lyakhovsky and Del Olmo, are presented. Explicit form of twisting elements are given and it is shown that the new twists as well as peripheric extended twists are suitable to deform inhomogeneous Lie algebras such as isu(n), iso(n), (1 + n) dimensional Schrödinger algebras and Poincaré algebra.
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تاریخ انتشار 2015