Pointed Hopf algebras over the sporadic simple groups.

DOI10.1016/j.jalgebra.2010.10.019zbMath1217.16026arXiv1001.1108OpenAlexW1994026942MaRDI QIDQ630857

Nicolás Andruskiewitsch, Matías Graña, Leandro Vendramin, Fernando Fantino

Publication date: 22 March 2011

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

Full work available at URL: https://arxiv.org/abs/1001.1108

zbMATH Keywords

group-like elementssporadic simple groupsYetter-Drinfeld modulesracksbraided Hopf algebrasfinite-dimensional Hopf algebraspointed Hopf algebrasNichols algebras

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Group rings (16S34) Computational aspects of associative rings (general theory) (16Z05) Hopf algebras and their applications (16T05)

Related Items (18)

The classification of Nichols algebras over groups with finite root system of rank two ⋮ ON THE CLASSIFICATION OF QUANDLES OF LOW ORDER ⋮ The cohomology ring of the 12-dimensional Fomin-Kirillov algebra ⋮ Divisibility relations for the dimensions and Hilbert series of Nichols algebras of non-Abelian group type. ⋮ 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 or copointed Hopf algebras over affine racks. ⋮ 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 ⋮ The logbook of pointed Hopf algebras over the sporadic simple groups. ⋮ Braided racks, Hurwitz actions and Nichols algebras with many cubic relations. ⋮ Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type VI. Suzuki and Ree groups ⋮ Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type. I: Non-semisimple classes in \(\mathbf{PSL}_n(q)\). ⋮ On finite-dimensional copointed Hopf algebras over dihedral groups ⋮ A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups ⋮ Finite-dimensional pointed Hopf algebras with alternating groups are trivial. ⋮ Pointed Hopf algebras over some sporadic simple groups. ⋮ Finite dimensional Nichols algebras over certainp-groups

Uses Software

• GAP
• GAP Character Table Library
• CTblLib
• AtlasRep
• ATLAS Group Representations

Cites Work

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• Finite-dimensional pointed Hopf algebras with alternating groups are trivial.
• The logbook of pointed Hopf algebras over the sporadic simple groups.
• Classification of arithmetic root systems
• On the classification of finite-dimensional pointed Hopf algebras.
• Pointed Hopf algebras over some sporadic simple groups.
• Simple quandles
• Quantum groups and quantum shuffles
• From racks to pointed Hopf algebras
• Root systems and Weyl groupoids for Nichols algebras
• The Nichols algebra of a semisimple Yetter-Drinfeld module
• On Nichols algebras over SL(2,Fq) and GL(2,Fq)
• ON POINTED HOPF ALGEBRAS ASSOCIATED WITH THE MATHIEU SIMPLE GROUPS
• A characterization of the borel-like subalgebras of quantum enveloping algebras
• On pointed Hopf algebras associated to some conjugacy classes in 𝕊_{𝕟}
• Introduction to quantum groups

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