We present natural families of coordinate algebras of noncommutative products of Euclidean spaces. These coordinate algebras are quadratic ones associated with an Rmatrix which is involutive and satisfies the YangBaxter equations. As a consequence they enjoy a list of nice properties, being regular of finite global dimension. Notably, we have eightdimensional noncommutative euclidean spaces which are particularly well behaved and are parametrised by a twodimensional sphere. Quotients include noncommutative sevenspheres 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.
You are here
Noncommutative products of Euclidean spaces
Research Group:
Giovanni Landi
Institution:
University of Trieste
Location:
A136
Schedule:
Wednesday, September 6, 2017  11:00
Abstract:
Openings
 Public calls for academic personnel (Permanent positions)
 Professors (Temporary/Researchers/Visiting Professors)
 SISSA Mathematical Fellowships
 Post Doctoral Fellowships
 PhD Scholarships
 Call for Applications (PhD)
 Undergraduate Fellowships
 Postgraduate Fellowships
 Master of Science in Mathematics
 Marie SklodowskaCurie Grants
Upcoming events

Alberto Maspero
Birkhoff coordinates for the Toda lattice in the limit of infinitely many particles with an application to FPU
Monday, March 19, 2018  10:00

Koen van den Dungen
The Kasparov product on open manifolds
Monday, March 19, 2018  14:00 to 15:30

Simone Di Marino
Sobolev spaces and nonlocal functionals in metric measure spaces
Tuesday, March 20, 2018  16:00

Lothar Göttsche
Virtual topological invariants of moduli spaces
Thursday, March 22, 2018  14:00
Recent publications

G. Cotti; B. Dubrovin; D. Guzzetti,Local moduli of semisimple Fro...

A. Michelangeli; A. Ottolini; R. Scandone,Fractional powers and singular...

M. Caponi,Existence of solutions to a ph...

I. Martini; B. Haasdonk; G. Rozza,Certified Reduced Basis Approx...