2024/12/23 by María Alejandra Alvarez, Salim Rivière, Alvarez, Maria Alejandra +7
Materials Science · #17B56 #FOS: Mathematics #K-Theory and Homology (math.KT) #Material Properties and Applications #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2412.17914
openalex publication_date 2024/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We exhibit in this article a contraction of the direct product Lie algebra g⊕ g of a finite-dimensional complex Lie algebra g onto the semi-direct product Lie algebra g\rtimes g, where the first factor g is viewed as a trivial Lie algebra and as the adjoint g-module. This contraction gives rise to a non-zero cohomology class in the second cohomology space. We generalize to the setting of h⊕ g and h\rtimes g with respect to a given crossed module of Lie algebras h→ g. We give many examples to illustrate our results.