Twist quantization of string and Hopf algebraic symmetry.
Universal envelopes of Malcev algebras: pointed Moufang bialgebras.
Weak multiplier Hopf algebras. Preliminaries, motivation and basic examples
Let G be a finite group. Consider the algebra A of all complex functions on G (with pointwise product). Define a coproduct Δ on A by Δ(f)(p,q) = f(pq) where f ∈ A and p,q ∈ G. Then (A,Δ) is a Hopf algebra. If G is only a groupoid, so that the product of two elements is not always defined, one still can consider A and define Δ(f)(p,q) as above when pq is defined. If we let Δ(f)(p,q) = 0 otherwise, we still get a coproduct on A, but Δ(1) will no longer be the identity in A ⊗ A. The pair (A,Δ)...
Yetter-Drinfeld-Long bimodules are modules
Let be a finite-dimensional bialgebra. In this paper, we prove that the category of Yetter-Drinfeld-Long bimodules, introduced by F. Panaite, F. Van Oystaeyen (2008), is isomorphic to the Yetter-Drinfeld category over the tensor product bialgebra as monoidal categories. Moreover if is a finite-dimensional Hopf algebra with bijective antipode, the isomorphism is braided. Finally, as an application of this category isomorphism, we give two results.
-Minkowski spacetimes and DSR algebras: fresh look and old problems.