Noncommutative Euclidean spaces

作者：Dubois Violette Michel^*; Landi Giovanni

来源：Journal of Geometry and Physics, 2018, 130: 315-330.

DOI：10.1016/j.geomphys.2018.04.006

• Noncommutative Euclidean spaces
• Noncommutative tori. Yang-Baxter equations

We give a definition of noncommutative finite-dimensional Euclidean spaces R-n. We then remind our definition of noncommutative products of Euclidean spaces R(N)1 and R(N)2 which produces noncommutative Euclidean spaces RN1+N2. We solve completely the conditions defining the noncommutative products of the Euclidean spaces RNI and R(N)2 and prove that the corresponding noncommutative unit spheres SN1+N2-1 are noncommutative spherical manifolds. We then apply these concepts to define "noncommutative" quaternionic planes and noncommutative quaternionic tori on which acts the classical quaternionic torus T-H(2) = U-1(H) x U-1(H).

• 出版日期2018-8