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<p>Motivated by the work of Gerstenhaber-Voronov and that of Malvenuto-Reuternauer, we define on pointed multiplicative operads in the category of vector spaces over an arbitrary ground field <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40062_2025_372_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {K}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">K</mi> </math></EquationSource> </InlineEquation>, a cosimplicial vector space structure. This permits us to construct on such operads some algebraic structures such as the homotopy G-algebra and the bicomplex algebra structures. Moreover we illustrate our constructions through some examples and explain or extend some well-known results.</p>

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Cosimplicial structure on pointed multiplicative operads

  • 期刊论文

  • 发表日期：

    2025年6月17日

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  • V. Jacky III Batkam Mbatchou,
  • Calvin Tcheka

摘要

Motivated by the work of Gerstenhaber-Voronov and that of Malvenuto-Reuternauer, we define on pointed multiplicative operads in the category of vector spaces over an arbitrary ground field \(\mathbb {K}\) K , a cosimplicial vector space structure. This permits us to construct on such operads some algebraic structures such as the homotopy G-algebra and the bicomplex algebra structures. Moreover we illustrate our constructions through some examples and explain or extend some well-known results.