Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type. I: Non-semisimple classes in \(\mathbf{PSL}_n(q)\).

DOI10.1016/j.jalgebra.2014.06.019zbMath1338.16034arXiv1312.6238OpenAlexW2041237263WikidataQ105627896 ScholiaQ105627896MaRDI QIDQ492983

Giovanna Carnovale, Nicolás Andruskiewitsch, Gastón Andrés García

Publication date: 11 September 2015

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.6238

zbMATH Keywords

group algebrasgroup-like elementsYetter-Drinfeld modulespointed Hopf algebrasfinite simple groups of Lie typeNichols algebras

Mathematics Subject Classification ID

Hopf algebras and their applications (16T05)

Related Items (12)

Pointed Hopf algebras with triangular decomposition. A characterization of multiparameter quantum groups ⋮ Finite dimensional Hopf algebras over Kac-Paljutkin algebra $H_8$ ⋮ Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type. V: Mixed classes in Chevalley and Steinberg groups ⋮ Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type. IV: Unipotent classes in Chevalley and Steinberg groups ⋮ Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type VII. Semisimple classes in \(\mathbf{PSL}_n (q)\) and \(\mathbf{PSp}_{2n}(q)\) ⋮ Finite GK-dimensional Nichols algebras over the infinite dihedral group ⋮ Projective class rings of the category of Yetter-Drinfeld modules over the 2-rank taft algebra ⋮ Duality for infinite-dimensional braided bialgebras and their (co)modules ⋮ Finite-dimensional Hopf algebras over the Hopf algebra \(H_{d:-1,1}\) of Kashina ⋮ Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type VI. Suzuki and Ree groups ⋮ Finite-dimensional Hopf algebras over the Hopf algebra \(H_{b:1}\) of Kashina ⋮ On some classification of finite-dimensional Hopf algebras over the Hopf algebra Hb:1* of Kashina

Cites Work

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• Finite-dimensional pointed Hopf algebras with alternating groups are trivial.
• Pointed Hopf algebras over the sporadic simple groups.
• Classification of arithmetic root systems
• On the classification of finite-dimensional pointed Hopf algebras.
• Simple quandles
• From racks to pointed Hopf algebras
• Finite quantum groups and Cartan matrices
• Finite Weyl groupoids of rank three
• On Nichols algebras associated to simple racks
• Root systems and Weyl groupoids for Nichols algebras
• The Nichols algebra of a semisimple Yetter-Drinfeld module
• On twisted conjugacy classes of type D in sporadic simple groups
• On Nichols algebras over SL(2,Fq) and GL(2,Fq)
• ON NICHOLS ALGEBRAS OVER PGL(2, q) AND PSL(2, q)
• The Finite Simple Groups
• Centralizers of Semisimple Elements in the Finite Classical Groups
• Bialgebras of type one^*
• On Pointed Hopf Algebras of Dimension 2 ⁿ
• Finite quantum groups over abelian groups of prime exponent
• On Twisted homogeneous racks of type D

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