Pointed hopf algebras

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August undefined, 2024

Pointed Hopf algebras. This is a survey on pointed Hopf algebras over algebraically closed fields of characteristic 0. We propose to classify pointed Hopf algebras by first determining the graded Hopf algebra $\gr A$ associated to the coradical filtration of . http://library.msri.org/books/Book43/files/andrus.pdf

[2301.03361] Finite-dimensional pointed Hopf algebras over finite ...

Webthese are the pointed Hopf algebras arising in Andruskiewitsch and Schneider’s classi cation of nite dimensional pointed Hopf algebras, but with more general groups of grouplikes allowed. In Section 8 we give in Theorem 8.1 necessary and su cient conditions for U(D; ) to be a PI-algebra and study delta sets. WebSep 3, 2024 · Abstract For a class of neither pointed nor semisimple Hopf algebras $H_ {4n}$ of dimension $4n$, it is shown that they are quasi-triangular, which universal $R$-matrices are described. The... is an oz more than a gram

Generalized Hopf–Ore Extensions of Hopf Group-Coalgebras

WebAbstract This thesis is concerned with properties of pointed Hopf algebras: that is, Hopf algebras whose coradicals are the group algebras of their grouplike elements. These have WebMar 15, 2000 · Google Scholar. 16. S. Montgomery. Classifying finite dimensional semisimple Hopf algebras. Trends in the Representation Theory of Finite-dimensional Algebras, Proceedings of the AMS-IMS-SIAM Summer Research Conference on Finite Dimensional Algebras, Seattle, 1997, 229, AMS Contemp. Math ( 1998) p. 265–279. … Webclassiﬁed all ﬁnite dimensional pointed Hopf algebras having abelian groups of grouplike elements, under a mild condition on the group orders. These include Lusztig’s small … olympus 25 f1 8

(PDF) About finite dimensional Hopf algebras - ResearchGate

[math/0110136] Pointed Hopf algebras - arXiv.org

Webﬁnite dimensional pointed Hopf algebras of rank one over an algebraically closed ﬁeld of characteristic zero by using group datums. Scherotzke [17] classiﬁed such Hopf algebras for the case of char(k) = p > 0. It was proven in [12, 17] that a ﬁnite dimensional pointed Hopf algebra of rank one over an algebraically closed ﬁeld is olympus 24mm f18 micro 4 3WebMay 25, 2024 · This is a contribution to the classification of finite-dimensional pointed Hopf algebras in positive characteristic. Beyond the classical theme of cocommutative Hopf algebras—see, for instance, [ CF] and the references therein—the problem was considered in several recent works [ CLW, HW, NW, NWW1, NWW2, W ]. is an personal loan variable or fixed rate

"WebMay 1, 2024 · We describe all finite-dimensional pointed Hopf algebras whose infinitesimal braiding is a fixed Yetter-Drinfeld module decomposed as the sum of two simple objects: a point and the one of transpositions of the symmetric group in three letters. " - Pointed hopf algebras

Pointed hopf algebras

WebJan 9, 2024 · We conclude that any finite-dimensional pointed Hopf algebra H with group of grouplike elements isomorphic to PSL (n,q) (n greater than or equal to 4), PSL (3,q) (q greater than 2), or PSp (2n,q) (n greater than or equal to 3), is isomorphic to a group algebra, completing work in arXiv:1506.06794 . Submission history Webintroduction to the modern classification theory of pointed Hopf algebras for advanced graduate students and researchers working in categorial aspects and classification theory of Hopf algebras and their generalization. Transactions of the American Nuclear Society - Nov 05 2024 Local Bifurcation and Symmetry - Apr 10 2024

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WebHopf algebras occur naturally in algebraic topology, where they originated and are related to the H-space concept, in group scheme theory, in group theory (via the concept of a group … WebThe class of nite-dimensional pointed Hopf algebras is the best understood and the subclass of those with abelian group of group-like elements is the only one whose classi ca-tion is essentially complete. Theorem 1.2.1 goes beyond the situation treated in [MPSW] but uses the same approach to the classi cation of pointed Hopf algebras proposed in

WebJan 3, 2024 · We examine actions of finite-dimensional pointed Hopf algebras on central simple division algebras in characteristic 0. (By a Hopf action we mean a Hopf module algebra structure.) In all examples considered, we show that the given Hopf algebra does admit a faithful action on a central simple division algebra, and we construct such a … WebThe class of nite-dimensional pointed Hopf algebras is the best understood and the subclass of those with abelian group of group-like elements is the only one whose classi ca-tion is essentially complete. Theorem 1.2.1 goes beyond the situation treated in [MPSW] but uses the same approach to the classi cation of pointed Hopf algebras proposed in

WebAug 10, 2015 · Namely, we study actions of finite dimensional (not necessarily semisimple) Hopf algebras on commutative domains, particularly when H is pointed of finite Cartan … WebA Hopf algebra is a bialgebra with an additional special map called the antipode. The special way in which coalgebras or better yet Hopf algebras arise in the study of the variety of fields is best displayed in combinatorics, where these …

Webin classifying f-d pointed Hopf algebras when is algebraically closed of characteristic 0 and G(A) is commutative with mild restrictions on jG(A)j [Andrus¡Schn 2010]. The similarities between these Hopf algebras and Lustig’s small quantum groups are striking.

WebThe classification of finite-dimensional pointed Hopf algebras with group was finished in [AHS]: there are exactly two of them, the bosonization of a Nichols algebra of dimension 12 and a non-trivial lifting. Here we … is an potato a vegetableWebIn this paper, the representation type of a class of pointed Hopf algebras is determined. As an application, all indecomposable modules of a simple-pointed Hopf algebra R (q,α) are classified. The Clebsch–Gordan-like formula for the decomposition of the tensor product, taken on the ground field, of two indecomposable modules of R (q,α) is ... is an plant cell prokaryotic or eukaryotichttp://personal.colby.edu/personal/c/cgbontea/CV2024.pdf is an potato a fruitWebWe show that all finite dimensional pointed Hopf algebras with the same diagram in the classification scheme of Andruskiewitsch and Schneider are cocycle deformations of … is an oyster shell a mineralWebFeb 1, 1978 · The algebra structure of a commutative pointed Hopf algebra A seems to be best understood by a detailed analysis of the coalgebra structure. If B C A is a sub-Hopf algebra and A0 C B, then A as a 5-algebra can be described in terms of … olympus 25mm f1.2 steve huffWebJan 7, 2010 · Title: Pointed Hopf algebras over the sporadic simple groups. Authors: N. Andruskiewitsch, F. Fantino, M. Graña, L. Vendramin. Download PDF Abstract: We show … olympus 25mm f1.2 proWebobjects called Hopf algebras Published results in peer-reviewed journals Disseminated results to peers at international and national meetings PUBLICATIONS 1. Pointed braided tensor categories, with D. Nikshych, Tensor categories and Hopf algebras, 67-94, Contemp. Math., 728, Amer. Math. Soc., Providence, RI, 2024. 2. olympus 24x wide