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.
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Noncommutative products of Euclidean spaces
Research Group:
Giovanni Landi
Institution:
University of Trieste
Location:
A136
Schedule:
Wednesday, September 6, 2017  11:00
Abstract:
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Massimiliano Berti
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Andrei Agrachev
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Ludwik Dabrowski
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Nicola Gigli
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Ugo Bruzzo
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Stefano Bianchini
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