Infinitesimal and tangent to polylogarithmic complexes for higher weight

Raziuddin Siddiqui; Raziuddin Siddiqui

doi:10.3934/math.2019.4.1248

AIMS Mathematics

2019, Volume 4, Issue 4: 1248-1257. doi: 10.3934/math.2019.4.1248

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Research article

Infinitesimal and tangent to polylogarithmic complexes for higher weight

Raziuddin Siddiqui ^,

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

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 $n$.
- polylogarithm,
- infinitesimal complex,
- five term relation,
- tangent complex
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

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Abstract

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 $n$.

References

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