Yetter–Drinfeld modules under cocycle twists
نویسندگان
چکیده
منابع مشابه
Yetter-drinfeld Modules under Cocycle Twists
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...
متن کاملBiproducts and Two-cocycle Twists of Hopf Algebras
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...
متن کاملCocycle Knot Invariants from Quandle Modules and Generalized Quandle Cohomology
Three new knot invariants are defined using cocycles of the generalized quandle homology theory that was proposed by Andruskiewitsch and Graña. We specialize that theory to the case when there is a group action on the coefficients. First, quandle modules are used to generalize Burau representations and Alexander modules for classical knots. Second, 2-cocycles valued in non-abelian groups are us...
متن کاملGeneralizations of Quandle Cocycle Invariants and Alexander Modules from Quandle Modules
Quandle cohomology theory was developed [5] to define invariants of classical knots and knotted surfaces in state-sum form, called quandle cocycle (knot) invariants. The quandle cohomology theory is a modification of rack cohomology theory which was defined in [11]. The cocycle knot invariants are analogous in their definitions to the Dijkgraaf-Witten invariants [8] of triangulated 3-manifolds ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2010
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2009.10.001