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Regular Seminar Mauricio Valenzuela (Chile Austral U., Valdivia)
The goal of this talk is to show some uses of the Gronewold-Moyal product in physics and new applications. In the first part of this talk we review the approach of Gronewold and Moyal in the quantization of classical systems. Then we remark algebraic aspects related to the representation of symplectic algebras and extensions of Anti-de-Sitter algebras. Subsequently we describe how these aspects are used in higher spin gravity. In the second part of this talk we present some new advances. We quantize a particular class of algebraic varieties, involving multivectors, and which contains Minkowski space slices. We show that these non-commutative geometries are solutions of known matrix models and some simple extensions of them. Then we present new models which describe the dynamics of extended objects in close resemblance to the equations of Hamiltonian systems. We also introduce statistical distributions in these spaces which encode their coordinates spectra.