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The interface of noncommutative geometry and physics
(2004-01)
As a mathematical theory per se, noncommutative geometry (NCG) is by now well established. From the beginning, its progress has been crucially influenced by quantum physics: we briefly review this development in recent ...
Hopf algebras in noncommutative geometry
(2003)
We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal ...
U(N) Yang-Mills in non-commutative space time
(Springer, 2019-04-08)
We present an approach to U ⋆ (N) Yang-Mills theory in non-commutative space based upon a novel phase-space analysis of the dynamical fields with additional auxiliary variables that generate Lorentz structure and colour ...
Interactions between non-commutative algebraic geometry and skew PBW extensions
(2016-08-11)
Abstract. We study some relations and interactions between non-commutative algebraic geometry and the skew PBW extensions. For this we will introduce a new class of noncommutative rings, the semi-graded rings, and for ...
Examples of noncommutative geometrical spaces
(2004-01)
We develop some examples of spectral triples in noncommutative geometry, on the theme of the noncommutative torus but with several variations.
States in generalized probabilistic models: An approach based in algebraic geometry
(De Gruyter, 2019-06)
We present a characterization of states in generalized probabilistic models by appealing to a non-commutative version of geometric probability theory based on algebraic geometry techniques. Our theoretical framework allows ...