Twistings, crossed coproducts and Hopf-Galois coextensions

Once again about quantum deformations of D=4 Lorentz algebra: twistings of q-deformation

This paper together with the previous one (arXiv:hep-th/0604146) presents the detailed description of all quantum deformations of D=4 Lorentz algebra as Hopf algebra in terms of complex and real generators. We describe here in detail two quantum deformations of the D=4 Lorentz algebra o(3,1) obtained by twisting of the standard q-deformation U_{q}(o(3,1)). For the first twisted q-deformation an Abelian twist depending on Cartan generators of o(3,1) is used. The second example of twisting provides a quantum deformation of Cremmer-Gervais type for the Lorentz algebra. For completeness we describ…

On Quasi-Hopf superalgebras

In this work we investigate several important aspects of the structure theory of the recently introduced quasi-Hopf superalgebras (QHSAs), which play a fundamental role in knot theory and integrable systems. In particular we introduce the opposite structure and prove in detail (for the graded case) Drinfeld's result that the coproduct $Δ' \equiv (S\otimes S)\cdot T\cdot Δ\cdot S^{-1}$ induced on a QHSA is obtained from the coproduct $Δ$ by twisting. The corresponding ``Drinfeld twist'' $F_D$ is explicitly constructed, as well as its inverse, and we investigate the complete QHSA associated with…

Coquasi-bialgebroids 与余循环扭曲

Coquasi-bialgebroids and cocycle twisting

引入非交换基代数上的 coquasi-bialgebroid，通过 Takeuchi 乘积和 3-余循环实现结合性，发展基本理论并证明卷积可逆 2-上链的扭曲定理，构造 Connes-Moscovici 型例子和有限群例子。

量子环面代数的张量积、$q$-特征标与$R$-矩阵

Tensor products, $q$-characters and $R$-matrices for quantum toroidal algebras

针对所有非扭型量子环面代数，引入基于反对合扭曲Drinfeld余积的新拓扑余积，定义可积表示范畴的张量积，证明其与Drinfeld多项式兼容等仿射层结果的量子环面类似物，还得到解Yang-Baxter方程的$R$-矩阵。