2014/12/12 by Dimitri Gurevich, Gurevich, D., Saponov, P.
Mathematics · Physics and Astronomy · #46L65 #46L87 #81T75 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1412.4014
openalex publication_date 2014/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of the paper is twofold. First, we introduce analogs of (partial) derivatives on certain Noncommutative algebras, including some enveloping algebras and their "braided counterparts", namely, the so-called modified Reflection Equation algebras. By using these derivatives we construct an analog of the de Rham complex on these algebras. Second, we discuss deformation property of some quantum algebras and show that contrary to a commonly held view, in the so-called q-Witt algebra there is no analog of the PBW theorem. In this connection, we discuss different forms of the Jacobi condition related to quadratic-linear algebras.