On finite GK-dimensional Nichols algebras over abelian groups

DOI10.1090/memo/1329OpenAlexW3192920745MaRDI QIDQ5020899

István Heckenberger, Nicolás Andruskiewitsch, Iván Ezequiel Angiono

Publication date: 7 January 2022

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.02521

zbMATH Keywords

Nichols algebraGelfand-Kirillov dimensionpointed Hopf algebraYetter-Drinfeld modulebraided vector space

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Ring-theoretic aspects of quantum groups (16T20) Research exposition (monographs, survey articles) pertaining to associative rings and algebras (16-02)

Related Items (19)

Multinomial expansion and Nichols algebras associated to non-degenerate involutive solutions of the Yang-Baxter equation ⋮ Finite dimensional Hopf algebras over Kac-Paljutkin algebra $H_8$ ⋮ Finite GK-dimensional pre-Nichols algebras of super and standard type ⋮ On non-connected pointed Hopf algebras of dimension 16 in characteristic 2 ⋮ On the Laistrygonian Nichols algebras that are domains ⋮ On the double of the (restricted) super Jordan plane ⋮ Representations of the super Jordan plane ⋮ Finite GK-dimensional pre-Nichols algebras of (super)modular and unidentified type ⋮ Finite GK-dimensional Nichols algebras over the infinite dihedral group ⋮ On finite GK-dimensional Nichols algebras of diagonal type: rank 3 and Cartan type ⋮ Rank 4 Nichols algebras of pale braidings ⋮ Duality for infinite-dimensional braided bialgebras and their (co)modules ⋮ Quotient Hopf algebras of the free bialgebra with PBW bases and GK-dimensions ⋮ Quantum groups -- algebra, analysis and category theory. Abstracts from the workshop held September 12--18, 2021 (hybrid meeting) ⋮ Nichols algebras that are quantum planes ⋮ On finite dimensional Nichols algebras of diagonal type ⋮ On the bosonization of the super Jordan plane ⋮ Liftings of Jordan and Super Jordan Planes ⋮ Examples of finite-dimensional pointed Hopf algebras in positive characteristic

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mini-workshop: Infinite dimensional Hopf algebras. Abstracts from the mini-workshop held April 13--19, 2014.
• Complete reducibility theorems for modules over pointed Hopf algebras.
• Noetherian Hopf algebra domains of Gelfand-Kirillov dimension two.
• A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems.
• Classification of arithmetic root systems
• Quasisymmetric and unipotent tensor categories
• Graded algebras of global dimension 3
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• A Hopf star-algebra of polynomials on the quantum \(SL(2,\mathbb{R})\) for a `unitary' \(R\)-matrix
• A \(*\)-product on SL(2) and the corresponding nonstandard quantum- U\(({\mathfrak sl}(2))\)
• Normal basis and transitivity of crossed products for Hopf algebras
• Quantum groups and quantum shuffles
• Co-Frobenius Hopf algebras and the coradical filtration
• A freeness theorem for Nichols algebras
• On a factorization of graded Hopf algebras using Lyndon words.
• PBW bases for a class of braided Hopf algebras.
• Yetter-Drinfeld modules over bosonizations of dually paired Hopf algebras.
• Hopf algebras of GK-dimension two with vanishing Ext-group
• An operator-theoretic approach to invariant integrals on quantum homogeneous \(\text{SU}_{n,1}\)-spaces
• Representations of a \(\mathbb Z/ 3\mathbb Z\)-quantum group
• The Weyl groupoid of a Nichols algebra of diagonal type
• Homological invariants relating the super Jordan plane to the Virasoro algebra
• Hopf algebras under finiteness conditions
• Properties of pointed and connected Hopf algebras of finite Gelfand-Kirillov dimension
• On Nichols algebras of diagonal type
• On two finiteness conditions for Hopf algebras with nonzero integral
• The Nichols algebra of a semisimple Yetter-Drinfeld module
• Classification of hyperbolic Dynkin diagrams, root lengths and Weyl group orbits
• Prime regular Hopf algebras of GK-dimension one
• On Noetherian affine prime regular Hopf algebras of Gelfand-Kirillov dimension 1
• On the quantization of certain Lie groups and algebras
• Crossed products for pointed hopf algebras
• A characterization of quantum groups
• A characterization of the borel-like subalgebras of quantum enveloping algebras
• Liftings of Jordan and Super Jordan Planes
• On finite GK-dimensional Nichols algebras of diagonal type
• Homological integral of Hopf algebras
• NOETHERIAN HOPF ALGEBRAS
• Noetherian Hopf algebras
• Introduction to quantum groups
• Quantum symmetric algebras

This page was built for publication: On finite GK-dimensional Nichols algebras over abelian groups