论文标题
Gerstenhaber支架在Hopf代数和Hochschild共同体上
Gerstenhaber bracket on Hopf algebra and Hochschild cohomologies
论文作者
论文摘要
我们计算了塔夫特代数$ t_p $的Hopf代数和Hochschild共同体上的Gerstenhaber支架，任何整数$ P> 2 $，这是一个非Quasi-Triangular Hopf代数。我们表明，与所有已知的准三角霍夫夫代数一样，在$ t_p $的HOPF代数同胞中，支架确实为零。此示例是非Quasi-Triangular代数的第一个已知的括号计算。此外，我们在任何HOPF代数共同体上找到了与钢筋分辨率上的任何HOPF代数的HOPF代数共同体的一般公式，这让人联想到Gerstenhaber的Hochschild共同学的原始公式。
We calculate the Gerstenhaber bracket on Hopf algebra and Hochschild cohomologies of the Taft algebra $T_p$ for any integer $p>2$ which is a nonquasi-triangular Hopf algebra. We show that the bracket is indeed zero on Hopf algebra cohomology of $T_p$, as in all known quasi-triangular Hopf algebras. This example is the first known bracket computation for a nonquasi-triangular algebra. Also, we find a general formula for the bracket on Hopf algebra cohomology of any Hopf algebra with bijective antipode on the bar resolution that is reminiscent of Gerstenhaber's original formula for Hochschild cohomology.
