2000/10/06 by C. Burdik, Č. Burdík, A. P. Isaev +1 · 8 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Affine Lie algebra #Algebra over a field #Algebraic structures and combinatorial models #Commutator #Computer science #Current algebra #Differential operator #Extension (predicate logic) #Filtered algebra #Graded Lie algebra #Lie algebra #Lie conformal algebra #Lie superalgebra #Mathematics #Nonlinear Waves and Solitons #Operator algebra #Pure mathematics #Universal enveloping algebra #math.QA
paper · pdf · doi:10.1134/1.1432906
published in Physics of Atomic Nuclei 64(12), 2101-2104 (Pleiades Publishing) · 10 pages, LaTeX. Report given at XXIII Int. Colloquium on Group Theoretical Methods in Physics, July 31 - August 05, 2000, Dubna (Russia)
arxiv created 2000/10/06 · openalex publication_date 2001/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For a quantum Lie algebra Γ, let Γ^ be its exterior extension (the algebra Γ^ is canonically defined). We introduce a differential on the exterior extension algebra Γ^ which provides the structure of a complex on Γ^. In the situation when Γ is a usual Lie algebra, this complex coincides with the “standard complex.” The differential is realized as a commutator with a (BRST) operator Q in a larger algebra Γ^[Ω], with extra generators canonically conjugated to the exterior generators of Γ^. A recurrent relation which uniquely defines the operator Q is given.