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Noncommutative products of Euclidean spaces
- Source :
- Lett.Math.Phys., Lett.Math.Phys., 2018, 108 (11), pp.2491-2513. ⟨10.1007/s11005-018-1090-z⟩
- Publication Year :
- 2018
- Publisher :
- HAL CCSD, 2018.
-
Abstract
- We present natural families of coordinate algebras of noncommutative products of Euclidean spaces. These coordinate algebras are quadratic ones associated with an R-matrix which is involutive and satisfies the Yang-Baxter equations. As a consequence they enjoy a list of nice properties, being regular of finite global dimension. Notably, we have eight-dimensional noncommutative euclidean spaces which are particularly well behaved and are deformations parametrised by a two-dimensional sphere. Quotients include noncommutative seven-spheres as well as noncommutative "quaternionic tori". There is invariance for an action of $SU(2) \times SU(2)$ in parallel with the action of $U(1) \times U(1)$ on a "complex" noncommutative torus which allows one to construct quaternionic toric noncommutative manifolds. Additional classes of solutions are disjoint from the classical case.<br />v2: Modified Theorem 2.3 ; added Remark 2.4
- Subjects :
- High Energy Physics - Theory
family
quaternion
Yang-Baxter equations
dimension: 8
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
space: noncommutative
Disjoint sets
01 natural sciences
Global dimension
Matrix (mathematics)
Noncommutative Euclidean spaces
Noncommutative tori
Mathematics::Quantum Algebra
Mathematics - Quantum Algebra
dimension: 2
Noncommutative torus
Mathematical Physics
Physics
[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]
Noncommutative quaternionic tori
Yang–Baxter equations
Mathematical Physics (math-ph)
Mathematics - Rings and Algebras
U(1)
010307 mathematical physics
Yang-Baxter equation
FOS: Physical sciences
Noncommutative Euclidean space
algebra: noncommutative
Combinatorics
space: Euclidean
torus: noncommutative
0103 physical sciences
Euclidean geometry
FOS: Mathematics
Quantum Algebra (math.QA)
0101 mathematics
Quotient
Mathematics::Operator Algebras
010102 general mathematics
deformation
Statistical and Nonlinear Physics
Torus
Noncommutative geometry
R-matrix
High Energy Physics - Theory (hep-th)
SU(2)
Rings and Algebras (math.RA)
sphere
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Lett.Math.Phys., Lett.Math.Phys., 2018, 108 (11), pp.2491-2513. ⟨10.1007/s11005-018-1090-z⟩
- Accession number :
- edsair.doi.dedup.....2a93c5a10dd3d3cb2eda47d26a4295b5