The Manturov (2, 3)-group G 3 2 is the group generated by three elements a, b , and c with defining relations a 2 = b 2 = c 2 = ( abc ) 2 = 1. We explicitly calculate the Anick chain complex for G 3 2 by algebraic discrete Morse theory and evaluate the Hochschild cohomology groups of the group algebra $$\mathbb{k}G_3^2$$ k G 3 2 with coefficients in all 1-dimensional bimodules over a field $$\mathbb{k}$$ k of characteristic zero.

中文翻译：

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Manturov (2,3)-群的 Anick 复形和 Hochschild 上同调

Manturov (2, 3)-群 G 3 2 是由具有定义关系 a 2 = b 2 = c 2 = ( abc ) 2 = 1 的三个元素 a、b 和 c 生成的群。我们明确地计算了 Anick 链用代数离散莫尔斯理论计算 G 3 2 的复数，并评估群代数的 Hochschild 上同调群 $$\mathbb{k}G_3^2$$ k G 3 2 以及域上所有一维双模的系数 $$\ mathbb{k}$$ k 的特征零。