scholarly journals The Projective Class Rings of a family of pointed Hopf algebras of Rank two

2016 ◽  
Vol 23 (5) ◽  
pp. 693-711 ◽  
Author(s):  
Hui-Xiang Chen ◽  
Hassen Suleman Esmael Mohammed ◽  
Weijun Lin ◽  
Hua Sun
Keyword(s):  
Hopf Algebras ◽  
Projective Class ◽  
Pointed Hopf Algebras

scholarly journals Bialgebra cohomology, pointed Hopf algebras, and deformations

2009 ◽  
Vol 213 (7) ◽  
pp. 1399-1417 ◽  
Author(s):  
Mitja Mastnak ◽  
Sarah Witherspoon
Keyword(s):  
Hopf Algebras ◽  
Pointed Hopf Algebras

scholarly journals EXAMPLES OF FINITE-DIMENSIONAL POINTED HOPF ALGEBRAS IN CHARACTERISTIC 2

2020 ◽  
pp. 1-14
Author(s):  
NICOLÁS ANDRUSKIEWITSCH ◽  
DIRCEU BAGIO ◽  
SARADIA DELLA FLORA ◽  
DAIANA FLÔRES
Keyword(s):  
Hopf Algebras ◽  
Abelian Groups ◽  
Vector Spaces ◽  
Group Algebras ◽  
Finite Abelian Groups ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras ◽  
Characteristic 2 ◽  
Nichols Algebras ◽  
Kirillov Dimension

Abstract We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.

EXT ALGEBRA OF NICHOLS ALGEBRAS OF CARTAN TYPE A2

2013 ◽  
Vol 12 (04) ◽  
pp. 1250191
Author(s):  
XIAOLAN YU ◽  
YINHUO ZHANG
Keyword(s):  
Spectral Sequence ◽  
Hopf Algebras ◽  
Type A ◽  
Serre Spectral Sequence ◽  
Nichols Algebra ◽  
Cartan Type ◽  
Dynkin Diagrams ◽  
Full Structure ◽  
Pointed Hopf Algebras ◽  
Nichols Algebras

We give the full structure of the Ext algebra of any Nichols algebra of Cartan type A2 by using the Hochschild–Serre spectral sequence. As an application, we show that the pointed Hopf algebras [Formula: see text] with Dynkin diagrams of type A, D, or E, except for A1 and A1 × A1 with the order NJ > 2 for at least one component J, are wild.

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 Pointed Hopf algebras over the sporadic simple groups

2011 ◽  
Vol 325 (1) ◽  
pp. 305-320 ◽  
Author(s):  
N. Andruskiewitsch ◽  
F. Fantino ◽  
M. Graña ◽  
L. Vendramin
Keyword(s):  
Hopf Algebras ◽  
Simple Groups ◽  
Pointed Hopf Algebras ◽  
Sporadic Simple Groups

scholarly journals On pointed Hopf algebras of dimension $p^n$

1999 ◽  
Vol 128 (2) ◽  
pp. 361-367 ◽  
Author(s):  
M. Beattie ◽  
S. Dăscălescu ◽  
L. Grünenfelder
Keyword(s):  
Hopf Algebras ◽  
Pointed Hopf Algebras
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