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The Koszul–Tate type resolution for Gerstenhaber–Batalin–Vilkovisky algebras
Journal of Homotopy and Related Structures ( IF 0.7 ) Pub Date : 2018-10-25 , DOI: 10.1007/s40062-018-0218-2
Jeehoon Park , Donggeon Yhee

Tate provided an explicit way to kill a nontrivial homology class of a commutative differential graded algebra over a commutative noetherian ring R in Tate (Ill J Math 1:14–27, 1957). The goal of this article is to generalize his result to the case of GBV (Gerstenhaber–Batalin–Vilkovisky) algebras and, more generally, the descendant \(L_\infty \)-algebras. More precisely, for a given GBV algebra \((\mathcal {A}=\oplus _{m\ge 0}\mathcal {A}_m, \delta , \ell _2^\delta )\), we provide another explicit GBV algebra \((\widetilde{\mathcal {A}}=\oplus _{m\ge 0}\widetilde{\mathcal {A}}_m, \widetilde{\delta }, \ell _2^{\widetilde{\delta }})\) such that its total homology is the same as the degree zero part of the homology \(H_0(\mathcal {A}, \delta )\) of the given GBV algebra \((\mathcal {A}, \delta , \ell _2^\delta )\).

中文翻译:

Gerstenhaber-Batalin-Vilkovisky代数的Koszul-Tate类型解析

泰特(Tate)提供了一种明确的方法,可以杀死泰特(Tate)中可交换Noether环R上的可交换差分梯度代数的非平凡同源性类(《国际数学杂志》 1957年1月14日至27日)。本文的目的是将其结果推广到GBV(Gerstenhaber–Batalin–Vilkovisky)代数的情况,以及更普遍的后代\(L_ \ infty \)-代数的情况。更精确地,对于给定的GBV代数\((\ mathcal {A} = \ oplus _ {m \ ge 0} \ mathcal {A} _m,\ delta,\ ell _2 ^ \ delta} \),我们提供了另一个显式GBV代数\((\\\\\ {{\ mathcal {A}} = \\ oplus _ {m \ ge 0} \\\\\\\\\ {{\ a}} _ m,\\\\\\\\ {{ \ delta}})\)使得其总同源性与给定GBV代数\ {(\ mathcal {A},\ delta,\ ell的同源性\(H_0(\ mathcal {A},\ delta)\)的度数零部分相同_2 ^ \ delta)\)
更新日期:2018-10-25
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