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Braided symmetric and exterior algebras II: Flat modules and Poisson structures

SPEAKER: Sebastian Zwicknagl

TITLE: Braided Symmetric and Exterior algebras II: Flat modules and Poisson structures

ABSTRACT The talk will be devoted to describing under which conditions a module over a quantum group is flat; i.e, its braided symmetric and exterior algebra are flat deformations of the ( classical) symmetric algebra over its classical limit. After briefly recalling definitions, we will describe how flatness is related to the existence of a Poisson-bracket on the symmetric algebra over the classical limit of the module. In order to efficiently classify potentially flat modules we will investigate how such structures arise. As an application we will classify the flat finite-dimensional modules over the quantized universal envelopping algebra of $sl_n (C)$.