On PBW-deformations of braided exterior algebras (Q1728193)

The author classifies PBW-deformations of certain exterior algebras. In particular, he focuses on deformations of quadratic-constant type, which correspond to Clifford algebras. A PBW-deformation of a quadratic algebra is a filtered algebra such that its associated graded algebra coincides with the original quadratic one (see for example [\textit{A. Braverman} and \textit{D. Gaitsgory}, J. Algebra 181, No. 2, 315--328 (1996; Zbl 0860.17002)]). The author looks for PBW-deformations of braided exterior algebras corresponding to certain modules of \(U_{q}(\mathfrak{sl}_{N})\). In the main result, a one-parameter family of PBW-deformations is found and it is verified that all of them are isomorphic as \(U_{q}(\mathfrak{sl}_{N})\)-module algebras. The paper is reader friendly and all necessary concepts are explained with proper references.