The four-dimensional Sklyanin algebras

DOI10.1007/BF00962090zbMath0809.16051MaRDI QIDQ1327526

S. Paul. Smith

Publication date: 29 March 1995

Published in: \(K\)-Theory (Search for Journal in Brave)

zbMATH Keywords

surveyregularitycyclic moduleselliptic curveHilbert seriesline bundleirreducible modulesSklyanin algebrasprojective varietypoint modulescategory of finitely generated graded modulesgraded noncommutative algebrasirreducible finite dimensional \(A\)-modulesYang- Baxter equation

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Finite rings and finite-dimensional associative algebras (16P10) Elliptic curves (14H52) Graded rings and modules (associative rings and algebras) (16W50) Homological dimension in associative algebras (16E10) Noetherian rings and modules (associative rings and algebras) (16P40)

Related Items (16)

The rational Sklyanin algebra and the Wilson and para-Racah polynomials ⋮ Cocycle twists of 4-dimensional Sklyanin algebras ⋮ Exotic elliptic algebras ⋮ Twisted homogeneous coordinate rings of abelian surfaces via mirror symmetry ⋮ Noncommutative quadric surfaces ⋮ Noncommutative geometry of homogenized quantum \(\mathfrak{sl}(2, \mathbb{C})\) ⋮ Interactions between algebraic geometry and noncommutative algebra. Abstracts from the workshop held May 1--7, 2022 ⋮ Lectures on Poisson Algebras ⋮ Elliptic R-matrices and Feigin and Odesskii's elliptic algebras ⋮ Unnamed Item ⋮ Noncommutative curves and noncommutative surfaces ⋮ Exotic elliptic algebras of dimension 4. With an appendix by Derek Tomlin ⋮ Superpotentials and higher order derivations. ⋮ Computation of point modules of finitely semi-graded rings ⋮ Noncommutative Homological Mirror Functor ⋮ Degenerate Sklyanin algebras, Askey–Wilson polynomials and Heun operators

Cites Work

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• Irreducible representations of the \(4\)-dimensional Sklyanin algebra at points of infinite order
• Twisted homogeneous coordinate rings
• Faisceaux algébriques cohérents
• Some algebraic structures connected with the Yang-Baxter equation. Representations of quantum algebras
• Graded algebras of global dimension 3
• Modules over regular algebras of dimension 3
• The center of the \(3\)-dimensional and \(4\)-dimensional Sklyanin algebras
• Dynamical symmetry of integrable quantum systems
• Partition function of the eight-vertex lattice model
• Some properties of non-commutative regular graded rings
• Auslander-Regular Algebras and Maximal Orders
• Modules over the 4-dimensional Sklyanin algebra

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