AIMS Mathematics, 2019, 4(4): 1248-1257. doi: 10.3934/math.2019.4.1248

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Infinitesimal and tangent to polylogarithmic complexes for higher weight

Department of Mathematical Sciences, Institute of Business Administration, Karachi, Pakistan

Motivic and polylogarithmic complexes have deep connections with $K$-theory. This article gives morphisms (different from Goncharov's generalized maps) between $\Bbbk$-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 $T\mathcal{B}_n(\Bbbk)$. These tangent groups develop the tangent to Goncharov's complex for weight $n$.
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