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

Quotients of hopf algebras

1978 ◽  
Vol 6 (17) ◽  
pp. 1789-1800 ◽  
Author(s):  
Warren D. Nichols
Keyword(s):  
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 Palatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1309
Author(s):  
Jerzy Lukierski
Keyword(s):  
Phase Space ◽  
Hopf Algebras ◽  
Deformation Parameter ◽  
Heisenberg Algebra ◽  
Planck Length ◽  
Covariant Quantum ◽  
Drinfeld Twist ◽  
Quantum Deformations ◽  
Heisenberg Double ◽  
Conformal Symmetries

We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed D=4 quantum inhomogeneous conformal Hopf algebras Uθ(su(2,2)⋉T4) and Uθ¯(su(2,2)⋉T¯4), where T4 describes complex twistor coordinates and T¯4 the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently, we introduce the quantum deformations of D=4 Heisenberg-conformal algebra (HCA) su(2,2)⋉Hℏ4,4 (Hℏ4,4=T¯4⋉ℏT4 is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length λp, is called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and the quantization map in Hℏ4,4. We also introduce generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebra Uθ(su(2,2)⋉T4).

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.

scholarly journals Cocycle deformations and Galois objects of semisimple Hopf algebras of dimension 16

2020 ◽  
Vol 48 (11) ◽  
pp. 4615-4637
Author(s):  
Rongchuan Xiong ◽  
Zhiqiang Yu
Keyword(s):  
Hopf Algebras
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