Research article

Infinitesimal and tangent to polylogarithmic complexes for higher weight

  • Received: 11 June 2019 Accepted: 11 August 2019 Published: 02 September 2019
  • MSC : 11G55, 19D, 18G

  • Motivic and polylogarithmic complexes have deep connections with $K$-theory. This article gives morphisms (different from Goncharov's generalized maps) between $\mathbb{k}$-vector spaces of Cathelineau's infinitesimal complex for weight $n$. Our morphisms guarantee that the sequence of infinitesimal polylogs is a complex. We are also introducing a variant of Cathelineau's complex with the derivation map for higher weight $n$ and suggesting the definition of tangent group $T\mathcal{B}_n(\mathbb{k})$. These tangent groups develop the tangent to Goncharov's complex for weight $n$.

    Citation: Raziuddin Siddiqui. Infinitesimal and tangent to polylogarithmic complexes for higher weight[J]. AIMS Mathematics, 2019, 4(4): 1248-1257. doi: 10.3934/math.2019.4.1248

    Related Papers:

  • Motivic and polylogarithmic complexes have deep connections with $K$-theory. This article gives morphisms (different from Goncharov's generalized maps) between $\mathbb{k}$-vector spaces of Cathelineau's infinitesimal complex for weight $n$. Our morphisms guarantee that the sequence of infinitesimal polylogs is a complex. We are also introducing a variant of Cathelineau's complex with the derivation map for higher weight $n$ and suggesting the definition of tangent group $T\mathcal{B}_n(\mathbb{k})$. These tangent groups develop the tangent to Goncharov's complex for weight $n$.


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  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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