Some remarks on q-deformed multiple polylogarithms
Some remarks on q-deformed multiple polylogarithms
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关于q变形多重多对数的一些评论
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
Karl
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文献类型：
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作者：
Karl
我们引入一般的q-变形的多重多项式，即使在双对数的情况下略有不同，通常在文献中讨论的变形。这里所建议的变形的优点是q-变形的多重多面体定义了一个代数，那么（就像在未变形的情况下一样）。对于q-变形的多重zeta-值的特殊情况，我们证明了甚至存在一个非交换和非余交换的Hopf代数结构，它是经典情况下交换Hopf代数结构的变形.最后，我们讨论了q-变形多重多项式与作者最近引入的一个非交换和非余交换的自对偶Hopf代数之间的可能对应关系，作为Grothendieck-Teichmueller群的量子模拟。
We introduce general q-deformed multiple polylogarithms which even in the dilogarithm case differ slightly from the deformation usually discussed in the literature. The merit of the deformation as suggested, here, is that q-deformed multiple polylogarithms define an algebra, then (as in the undeformed case). For the special case of q-deformed multiple zeta-values, we show that there exists even a noncommutative and noncocommutative Hopf algebra structure which is a deformation of the commutative Hopf algebra structure which one has in the classical case. Finally, we discuss the possible correspondence between q-deformed multiple polylogarithms and a noncommutative and noncocommutative self-dual Hopf algebra recently introduced by the author as a quantum analog of the Grothendieck-Teichmueller group.