Pointed hopf algebras

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August undefined, 2024

WebOct 12, 2001 · This is a survey on pointed Hopf algebras over algebraically closed fields of characteristic 0. We propose to classify pointed Hopf algebras $A$ by first determining … 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

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

WebIn the framework of the classification of finite-dimensional Hopf algebras, the interest in Ore’s extensions has been revived in the late 1990s by Beattie, Dăscălescu, Grünenfelder, Năstăsescu, and Nenciu, who took advantage of this construction to provide many new examples with special properties, such as pointed Hopf algebras, co ... Webclasses of noncocommutative Hopf algebras over a ﬁeld of characteristic 0. We prove ﬁnite generation of the cohomology ring of any ﬁnite dimensional pointed Hopf algebra, with abelian group of grouplike elements, under some mild re-strictions on the group order. Pointed Hopf algebras are precisely those whose sptl electricity

Bontea CV 2024, v.2

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 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... 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 … sheridan pickleball

Pointed hopf algebras

$HOPF ALGEBRAS arXiv:2304.04908v1 [math.QA] 11 Apr 2024$

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. … Webobjects called Hopf algebras Published results in peer-reviewed journals Disseminated results to peers at international and national meetings PUBLICATIONS 1. Pointed braided …

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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. WebJan 5, 2024 · Abstract Let $H$ be a pointed Hopf algebra with abelian coradical. Let $A\supseteq B$ be left (or right) coideal subalgebras of $H$ that contain the coradical of $H$. We show that $A$ has a PBW...

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. 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 …

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 WebA Hopf algebra is called pointed if all its simple left (or right) comodules are one-dimensional.The quantized enveloping algebras and Lusztig's small quantum groups are …

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WebHopf Algebras. The book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or … sheridan physical therapy sheridanWebApr 1, 1974 · JOURNAL OF ALGEBRA 28, 27-32 (1974) On Antipodes in Pointed Hopf Algebras EARL J. TAFT* AND ROBERT LEE WILSC^ Department of Mathematics, Rutgers, The State University, New Brunsivick, New Jersey 08903 Communicated by N. Jacobson Received June 10, 1972 If S is the antipode of a Hopf algebra H, the order of S is defined … sheridan pierceWebJan 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 sheridan physical therapy clinic sheridan arWebclassiﬁed 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 … sheridan physical therapyWebAug 5, 2024 · On pointed Hopf algebras over nilpotent groups. N. Andruskiewitsch; Mathematics. 2024; We classify finite-dimensional Nichols algebras over finite nilpotent … sptlights projectionWebintroduction to the modern classification theory of pointed Hopf algebras for advanced graduate students and researchers working in categorial aspects and classification theory … sptl isin codeWebWe show that all finite dimensional pointed Hopf algebras with the same diagram in the classification scheme of Andruskiewitsch and Schneider are cocycle deformations of … sptl lucknow