{
  "id": "2109.01972",
  "version": "v1",
  "published": "2021-09-05T02:45:20.000Z",
  "updated": "2021-09-05T02:45:20.000Z",
  "title": "Cohomology of weighted Rota-Baxter Lie algebras and Rota-Baxter paired operators",
  "authors": [
    "Apurba Das"
  ],
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "In this paper, we define representations and cohomology of weighted Rota-Baxter Lie algebras. As applications of cohomology, we study abelian extensions and formal $1$-parameter deformations weighted Rota-Baxter Lie algebras. Finally, we consider weighted Rota-Baxter paired operators that induces a weighted Rota-Baxter Lie algebra and a representation of it. We define suitable cohomology for such paired operators that govern deformation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-05T02:45:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B38",
      "17B56",
      "16S80"
    ],
    "keywords": [
      "cohomology",
      "deformations weighted rota-baxter lie algebras",
      "parameter deformations weighted rota-baxter lie",
      "study abelian extensions",
      "weighted rota-baxter paired operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}