Embedding a quantum nonsingular quadric in a quantum \(\mathbb{P}^3\)

DOI10.1006/jabr.1997.7077zbMath0910.16013OpenAlexW2016524584MaRDI QIDQ1369263

Kristel Van Rompay, Michaela Vancliff

Publication date: 16 February 1999

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

Full work available at URL: https://doi.org/10.1006/jabr.1997.7077

zbMATH Keywords

global dimensionHilbert seriesquadratic regular algebrastwisted homogeneous coordinate ringsnonsingular quadrics

Mathematics Subject Classification ID

Noncommutative algebraic geometry (14A22) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Elliptic curves (14H52) Graded rings and modules (associative rings and algebras) (16W50) Twisted and skew group rings, crossed products (16S35) Homological dimension in associative algebras (16E10) Low codimension problems in algebraic geometry (14M07)

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Cites Work

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• Irreducible representations of the \(4\)-dimensional Sklyanin algebra at points of infinite order
• Twisted homogeneous coordinate rings
• A two-parameter quantization of GL(n)
• Graded algebras of global dimension 3
• Modules over regular algebras of dimension 3
• Matrix-element bialgebras determined by quadratic coordinate algebras
• Quadratic algebras associated with the union of a quadric and a line in \(\mathbb{P}^ 3\)
• Segre product of Artin-Schelter regular algebras of dimension 2 and embeddings in quantum \(\mathbb{P}^ 3\)'s
• Central extensions of three dimensional Artin-Schelter regular algebras
• On Quantum Spaces of Lie Algebras
• Quantum deformations of GL_n
• Some properties of non-commutative regular graded rings
• Homogenized sl(2)
• Regularity of Algebras Related to the Sklyanin Algebra
• The Defining Relations of Quantum n × n Matrices
• Twisted Graded Algebras and Equivalences of Graded Categories
• Modules over the 4-dimensional Sklyanin algebra