Results 11 to 20 of about 105 (96)
Representations of Hopf-Ore Extensions of Group Algebras and Pointed Hopf Algebras of Rank One [PDF]
Algebras and Representation Theory, 2015 In this paper, we study the representation theory of Hopf-Ore extensions of group algebras and pointed Hopf algebras of rank one over an arbitrary field $k$. Let $H=kG( , a,\d)$ be a Hopf-Ore extension of $kG$ and $H'$ a rank one quotient Hopf algebra of $H$, where $k$ is a field, $G$ is a group, $a$ is a central element of $G$ and $ $ is a $k ...
Wang, Zhen, You, Lan, Chen, Hui-Xiang
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Constructing Pointed Hopf Algebras by Ore Extensions
Journal of Algebra, 2000 A general construction producing pointed co-Frobenius Hopf algebras is given, along with some classification results. This construction was used by the same authors to give a counterexample to Kaplansky's 10th conjecture [in the paper Invent. Math. 136, No. 1, 1-7 (1999; Zbl 0922.16021)].
Beattie, M +2 more
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From racks to pointed Hopf algebras
Advances in Mathematics, 2003 54 pages. Several minor corrections. Some references added.
Andruskiewitsch, N., Graña, M.
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Classification of pointed rank one Hopf algebras
Journal of Algebra, 2008 In this paper we classify the finite-dimensional pointed rank one Hopf algebras which are generated as algebras by the first element of the coradical filtration over a field of prime characteristic.
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Pointed Hopf algebras are free over Hopf subalgebras
Journal of Algebra, 1977 AbstractIt is well known that a commutative or cocommutative Hopf algebra is faithfully flat over any Hopf subalgebra. Examples of commutative cocommutative cosemisimple Hopf algebras have been found which are not free as modules over certain Hopf subalgebras.
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On antipodes in pointed Hopf algebras
Journal of Algebra, 1974 AbstractIf S is the antipode of a Hopf algebra H, the order of S is defined to be the smallest positive integer n such that Sn = I (in case such integers exist) or ∞ (if no such integers exist). Although in most familiar examples of Hopf algebras the antipode has order 1 or 2, examples are known of infinite dimensional Hopf algebras in which the ...
Taft, Earl J, Wilson, Robert Lee
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Module categories over pointed Hopf algebras [PDF]
Mathematische Zeitschrift, 2009 We develop some techniques to the study of exact module categories over some families of pointed finite-dimensional Hopf algebras. As an application we classify exact module categories over the tensor category of representations of the small quantum groups $u_q(\mathfrak{sl}_2)$.
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Pointed hopf algebras of dimension 32 [PDF]
Communications in Algebra, 2000 We give a complete classification of the 32-dimensional pointed Hopf algebras over an algebraically closed field k with characteristic different from 2. It turns out that there are infinite families of isomorphism classes of pointed Hopf algebras of dimension 32. In [Andruskiewitsch-Schneider, J. Alg 209], [Beattie-Dascalescu-Grunenfelder, Invent. Math.
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On pointed Hopf algebras over dihedral groups [PDF]
Pacific Journal of Mathematics, 2011 Let k be an algebraically closed field of characteristic 0 and let D_m be the dihedral group of order 2m with m= 4t, with t bigger than 2. We classify all finite-dimensional Nichols algebras over D_m and all finite-dimensional pointed Hopf algebras whose group of group-likes is D_m, by means of the lifting method.
Fantino, Fernando +1 more
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POINTED HOPF ACTIONS ON CENTRAL SIMPLE DIVISION ALGEBRAS [PDF]
Transformation Groups, 2022 23 ...
ETINGOF, P., NEGRON, C.
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