具有多重zeta值系数的Batalin-Vilkovisky代数上的泛A-infinity结构
量子代数
2018-08-24 v5 代数几何
摘要
我们显式构造了Batalin-Vilkovisky代数的一个泛A-infinity形变，其所有系数表示为多重zeta值的有理和。如果我们起始的Batalin-Vilkovisky代数是循环的，则该A-infinity形变也是循环的。此外，奇泊松括号的伴随作用作为A-infinity结构的导子而作用。该构造推测定义了Grothendieck-Teichmueller李代数的一个新表示。
引用
@article{arxiv.1501.02916,
title = {A universal A-infinity structure on Batalin-Vilkovisky algebras with multiple zeta value coefficients},
author = {Johan Alm},
journal= {arXiv preprint arXiv:1501.02916},
year = {2018}
}
备注
The "regularization map'' from gravity chord diagrams to prime chord diagrams does not respect cooperadic compositions (it only does so on the associated graded for the filtration by number of residual chords). This commpletely undermines the main construction. Thanks to Anton Khoroshkin for raising the issue