Embedding a quantum rank three quadric in a quantum P3

DOI10.1080/00927879908826599zbMath0936.16023OpenAlexW1995424120MaRDI QIDQ4254207

Michaela Vancliff, Brad Shelton

Publication date: 14 May 2000

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

Full work available at URL: https://doi.org/10.1080/00927879908826599

zbMATH Keywords

global dimensionstwisted homogeneous coordinate ringsquadric hypersurfacesquadratic Artin-Schelter regular algebras

Mathematics Subject Classification ID

Noncommutative algebraic geometry (14A22) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Graded rings and modules (associative rings and algebras) (16W50) Twisted and skew group rings, crossed products (16S35) Quadratic and Koszul algebras (16S37)

Related Items (17)

Cocycle twists of 4-dimensional Sklyanin algebras ⋮ Fat point modules over generalized Laurent polynomial rings. ⋮ Co-Point Modules Over Frobenius Koszul Algebras ⋮ SCHEMES OF LINE MODULES. II ⋮ Noncommutative quadric surfaces ⋮ Regular algebras of dimension 4 and their \(A_\infty\)-Ext-algebras. ⋮ A class of AS-regular algebras of dimension five. ⋮ The one-dimensional line scheme of a family of quadratic quantum \(\mathbb{P}^3\)s ⋮ Noncommutative curves and noncommutative surfaces ⋮ Exotic elliptic algebras of dimension 4. With an appendix by Derek Tomlin ⋮ Canonical maps to twisted rings. ⋮ Some finite quantum \(\mathbb{P}^3\)s that are infinite modules over their centers. ⋮ On Koszul algebras and a new construction of Artin-Schelter regular algebras ⋮ Generalized Laurent polynomial rings as quantum projective 3-spaces. ⋮ Quantum projective 3-spaces which embed weighted quantum planes. ⋮ Four dimensional regular algebras with point scheme, anonsingular quadric in P³ ⋮ Regular modules over 2-dimensional quantum Beilinson algebras of type \(S\)

Cites Work

• Graded algebras of global dimension 3
• Modules over regular algebras of dimension 3
• Quadratic algebras associated with the union of a quadric and a line in \(\mathbb{P}^ 3\)
• Embedding a quantum nonsingular quadric in a quantum \(\mathbb{P}^3\)
• Segre product of Artin-Schelter regular algebras of dimension 2 and embeddings in quantum \(\mathbb{P}^ 3\)'s
• Some properties of non-commutative regular graded rings
• Some quantum P³s with one point
• Regularity of Algebras Related to the Sklyanin Algebra
• Some quantum P³s with infinitely many points
• Koszul Duality Patterns in Representation Theory
• Twisted Graded Algebras and Equivalences of Graded Categories

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