The Manin Hopf algebra of a Koszul Artin-Schelter regular algebra is quasi-hereditary

DOI10.1016/j.aim.2016.09.017zbMath1405.16044arXiv1509.03157OpenAlexW2963504795MaRDI QIDQ340418

Theo Raedschelders, Michel Van den Bergh

Publication date: 14 November 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.03157

zbMATH Keywords

monoidal categoriesHopf algebrasquasi-hereditary algebras

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Rings arising from noncommutative algebraic geometry (16S38) Quantum groups (quantized function algebras) and their representations (20G42) Quadratic and Koszul algebras (16S37) Hopf algebras and their applications (16T05) Coalgebras and comodules; corings (16T15)

Related Items

V-universal Hopf algebras (co)acting on Ω-algebras, On the monoidal invariance of the cohomological dimension of Hopf algebras, Calabi-Yau property under monoidal Morita-Takeuchi equivalence, Algebras defined by Lyndon words and Artin-Schelter regularity, Universal constructions for Poisson algebras. Applications, Functors between representation categories. Universal modules, Equivalences of (co)module algebra structures over Hopf algebras, On quasi-hereditary algebras

Cites Work

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• On quantum groups associated to non-Noetherian regular algebras of dimension 2
• Skew Calabi-Yau algebras and homological identities.
• Grothendieck rings of universal quantum groups.
• Algebraic properties of Manin matrices. I
• Manin matrices, quantum elliptic commutative families and characteristic polynomial of elliptic Gaudin model
• Rational representations of algebraic groups: Tensor products and filtrations
• Graded algebras of global dimension 3
• Quasi-hereditary algebras
• Confluence and Koszulity
• The representation theory of non-commutative \(\mathcal{O}(\mathrm{GL}_2)\)
• Borel subalgebras redux with examples from algebraic and quantum groups
• Calabi-Yau algebras and superpotentials
• The quantum group of a preregular multilinear form.
• Rings with several objects
• The theory and practice of Reedy categories
• Representations of non-commutative quantum groups
• Koszul algebras and the quantum MacMahon master theorem
• Hopf bigalois extensions
• Co-representation theory of universal co-sovereign Hopf algebras
• Dualizing Complexes of Noetherian Complete Algebras via Coalgebras
• Cohomology of Groups in Arbitrary Categories
• Des catégories abéliennes