scholarly journals Automorphism group of representation ring of the weak Hopf algebra $\widetilde{H_8}$

2018 ◽  
Vol 68 (4) ◽  
pp. 1131-1148 ◽  
Author(s):  
Dong Su ◽  
Shilin Yang
Keyword(s):  
Automorphism Group ◽  
Hopf Algebra ◽  
Weak Hopf Algebra ◽  
Representation Ring

scholarly journals Rota-Baxter Leibniz Algebras and Their Constructions

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Liangyun Zhang ◽  
Linhan Li ◽  
Huihui Zheng
Keyword(s):  
Hopf Algebra ◽  
Weak Hopf Algebra ◽  
Associative Algebras ◽  
Leibniz Algebras

In this paper, we introduce the concept of Rota-Baxter Leibniz algebras and explore two characterizations of Rota-Baxter Leibniz algebras. And we construct a number of Rota-Baxter Leibniz algebras from Leibniz algebras and associative algebras and discover some Rota-Baxter Leibniz algebras from augmented algebra, bialgebra, and weak Hopf algebra. In the end, we give all Rota-Baxter operators of weight 0 and -1 on solvable and nilpotent Leibniz algebras of dimension ≤3, respectively.

On Braided Lie Structures of Algebras in the Categories of Weak Hopf Bimodules

2010 ◽  
Vol 17 (04) ◽  
pp. 685-698 ◽  
Author(s):  
Shuan-hong Wang ◽  
Hai-xing Zhu
Keyword(s):  
Hopf Algebra ◽  
Monoidal Category ◽  
Weak Hopf Algebra ◽  
Commutator Ideal ◽  
Commutative Subalgebras

Let H be a weak Hopf algebra. In this paper, it is proved that the monoidal category [Formula: see text] of weak Hopf bimodules studied in Wang [19] is equivalent to the monoidal category [Formula: see text] of weak Yetter–Drinfel'd modules introduced in Böhm [2]. When H has a bijective antipode, a braiding in the category [Formula: see text] is constructed by the braiding on [Formula: see text], generalizing the main result in Schauenburg [14]. Finally, the braided Lie structures of an algebra A in the category [Formula: see text] are investigated, by showing that if A is a sum of two braided commutative subalgebras, then the braided commutator ideal of A is nilpotent.

The Automorphism Group of Green Algebra of 9-Dimensional Taft Hopf Algebra

2020 ◽  
Vol 27 (04) ◽  
pp. 767-798
Author(s):  
Ruju Zhao ◽  
Chengtao Yuan ◽  
Libin Li
Keyword(s):  
Automorphism Group ◽  
Hopf Algebra ◽  
Real Number ◽  
Number Field ◽  
Direct Product ◽  
Quotient Group ◽  
Isomorphism Class ◽  
Dihedral Group ◽  
Green Ring ◽  
Real Number Field

Let H3 be the 9-dimensional Taft Hopf algebra, let [Formula: see text] be the corresponding Green ring of H3, and let [Formula: see text] be the automorphism group of Green algebra [Formula: see text] over the real number field ℝ. We prove that the quotient group [Formula: see text] is isomorphic to the direct product of the dihedral group of order 12 and the cyclic group of order 2, where T1 is the isomorphism class which contains the identity map and is isomorphic to a group [Formula: see text] with multiplication given by [Formula: see text].

scholarly journals Comparison of two notions of weak crossed product

2020 ◽  
pp. 2150059
Author(s):  
Jorge A. Guccione ◽  
Juan J. Guccione
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Crossed Product ◽  
Weak Hopf Algebra ◽  
Crossed Products ◽  
Hopf Algebroid ◽  
Hopf Algebroids ◽  
Weak Crossed Product ◽  
Cleft Extensions ◽  
Weak Hopf Algebras

We compare the restriction to the context of weak Hopf algebras of the notion of crossed product with a Hopf algebroid introduced in [Cleft extensions of Hopf algebroids, Appl. Categor. Struct. 14(5–6) (2006) 431–469] with the notion of crossed product with a weak Hopf algebra introduced in [Crossed products for weak Hopf algebras with coalgebra splitting, J. Algebra 281(2) (2004) 731–752].

Weak Hopf Algebra

2004 ◽  
pp. 503-503
Author(s):  
François Gieres ◽  
Fang Li ◽  
Peter Trotter
Keyword(s):  
Hopf Algebra ◽  
Weak Hopf Algebra

The Duality Theorem for Weak Hopf Algebra (Co) Actions

2010 ◽  
Vol 38 (12) ◽  
pp. 4613-4632 ◽  
Author(s):  
Xuan Zhou ◽  
Shuanhong Wang
Keyword(s):  
Hopf Algebra ◽  
Duality Theorem ◽  
Weak Hopf Algebra

scholarly journals Quantum Groupoids Acting on Semiprime Algebras

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Inês Borges ◽  
Christian Lomp
Keyword(s):  
Hopf Algebra ◽  
Polynomial Identity ◽  
Weak Hopf Algebra ◽  
Smash Product ◽  
Module Algebra

Following Linchenko and Montgomery's arguments we show that the smash product of an involutive weak Hopf algebra and a semiprime module algebra, satisfying a polynomial identity, is semiprime.

scholarly journals THE HOPF AUTOMORPHISM GROUP AND THE QUANTUM BRAUER GROUP IN BRAIDED MONOIDAL CATEGORIES

2013 ◽  
Vol 12 (06) ◽  
pp. 1250224
Author(s):  
B. FEMIĆ
Keyword(s):  
Automorphism Group ◽  
Hopf Algebra ◽  
Hopf Algebras ◽  
Brauer Group ◽  
Monoidal Categories ◽  
Brauer Groups ◽  
New Information ◽  
Braided Monoidal Categories ◽  
Usual Quantum ◽  
Module Algebras

With the motivation of giving a more precise estimation of the quantum Brauer group of a Hopf algebra H over a field k we construct an exact sequence containing the quantum Brauer group of a Hopf algebra in a certain braided monoidal category. Let B be a Hopf algebra in [Formula: see text], the category of Yetter–Drinfel'd modules over H. We consider the quantum Brauer group [Formula: see text] of B in [Formula: see text], which is isomorphic to the usual quantum Brauer group BQ(k; B ⋊ H) of the Radford biproduct Hopf algebra B ⋊ H. We show that under certain symmetricity condition on the braiding in [Formula: see text] there is an inner action of the Hopf automorphism group of B on the former. We prove that the subgroup [Formula: see text] — the Brauer group of module algebras over B in [Formula: see text] — is invariant under this action for a family of Radford biproduct Hopf algebras. The analogous invariance we study for BM(k; B ⋊ H). We apply our recent results on the latter group and generate a new subgroup of the quantum Brauer group of B ⋊ H. In particular, we get new information on the quantum Brauer groups of some known Hopf algebras.

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