The Defining Relations of Quantum n × n Matrices

DOI10.1112/jlms/52.2.255zbMath0837.16024OpenAlexW2171657721MaRDI QIDQ4864050

Michaela Vancliff

Publication date: 22 February 1996

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

Full work available at URL: https://doi.org/10.1112/jlms/52.2.255

zbMATH Keywords

automorphismsvarietypolynomial ringsPoisson structuresdefining relationssymplectic leavespoint modulescoordinate ring of quantum matricescoordinate ring of quantum \(n \times n\) matricesgraded flat deformationshomogeneous Poisson brackets

Mathematics Subject Classification ID

Noncommutative algebraic geometry (14A22) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Graded rings and modules (associative rings and algebras) (16W50) Automorphisms of curves (14H37) Twisted and skew group rings, crossed products (16S35) Low codimension problems in algebraic geometry (14M07)

Related Items (11)

Embedding a quantum nonsingular quadric in a quantum \(\mathbb{P}^3\) ⋮ Regular algebras of dimension 4 and their \(A_\infty\)-Ext-algebras. ⋮ A class of AS-regular algebras of dimension five. ⋮ Reflection groups and rigidity of quadratic Poisson algebras ⋮ A class of quadratic matrix algebras arising from the quantized enveloping algebra Uq(A2n−1) ⋮ Double Ore extensions. ⋮ Exotic elliptic algebras of dimension 4. With an appendix by Derek Tomlin ⋮ Some quantum P³s with infinitely many points ⋮ Double extension regular algebras of type (14641). ⋮ Four dimensional regular algebras with point scheme, anonsingular quadric in P³ ⋮ Symplectic ideals of poisson algebras and the poisson structure associated to quantum matrices

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