Principal homogeneous spaces for arbitrary Hopf algebras

1990 ◽  
Vol 72 (1-2) ◽  
pp. 167-195 ◽  
Author(s):  
Hans-Jürgen Schneider
Keyword(s):  
Hopf Algebras ◽  
Homogeneous Spaces

scholarly journals Plane Curves Which are Quantum Homogeneous Spaces

2021 ◽  
Author(s):  
Ken Brown ◽  
Angela Ankomaah Tabiri
Keyword(s):  
Hopf Algebras ◽  
Final Section ◽  
Homogeneous Spaces ◽  
Plane Curve ◽  
Plane Curves ◽  
Closed Field ◽  
Quantum Homogeneous Space ◽  
Central Elements ◽  
Pointed Hopf Algebras ◽  
Future Work

AbstractLet $\mathcal {C}$ C be a decomposable plane curve over an algebraically closed field k of characteristic 0. That is, $\mathcal {C}$ C is defined in k2 by an equation of the form g(x) = f(y), where g and f are polynomials of degree at least two. We use this data to construct three affine pointed Hopf algebras, A(x, a, g), A(y, b, f) and A(g, f), in the first two of which g [resp. f ] are skew primitive central elements, with the third being a factor of the tensor product of the first two. We conjecture that A(g, f) contains the coordinate ring $\mathcal {O}(\mathcal {C})$ O ( C ) of $\mathcal {C}$ C as a quantum homogeneous space, and prove this when each of g and f has degree at most five or is a power of the variable. We obtain many properties of these Hopf algebras, and show that, for small degrees, they are related to previously known algebras. For example, when g has degree three A(x, a, g) is a PBW deformation of the localisation at powers of a generator of the downup algebra A(− 1,− 1,0). The final section of the paper lists some questions for future work.

scholarly journals Quantum homogeneous spaces and quasi-Hopf algebras

2000 ◽  
pp. 105-121 ◽  
Author(s):  
Benjamin Enriquez ◽  
Yvette Kosmann-Schwarzbach
Keyword(s):  
Hopf Algebras ◽  
Homogeneous Spaces ◽  
Quantum Homogeneous Spaces

scholarly journals Quantum homogeneous spaces of connected Hopf algebras

2016 ◽  
Vol 454 ◽  
pp. 400-432 ◽  
Author(s):  
Ken Brown ◽  
Paul Gilmartin
Keyword(s):  
Hopf Algebras ◽  
Homogeneous Spaces ◽  
Quantum Homogeneous Spaces

Application of Morse theory to some homogeneous spaces

1969 ◽  
Vol 21 (3) ◽  
pp. 343-353 ◽  
Author(s):  
S. Ramanujan
Keyword(s):  
Morse Theory ◽  
Homogeneous Spaces

Left counital Hopf algebras on bi-decorated planar rooted forests and Rota-Baxter systems

2020 ◽  
Vol 27 (2) ◽  
pp. 219-243 ◽  
Author(s):  
Xiao-Song Peng ◽  
Yi Zhang ◽  
Xing Gao ◽  
Yan-Feng Luo
Keyword(s):  
Hopf Algebras

scholarly journals Monadic cointegrals and applications to quasi-Hopf algebras

2021 ◽  
Vol 225 (10) ◽  
pp. 106678
Author(s):  
Johannes Berger ◽  
Azat M. Gainutdinov ◽  
Ingo Runkel
Keyword(s):  
Hopf Algebras
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