SL_2（C）中平凡character的群与变形的恒等式
The parallelogram identity on groups and deformations of the trivial character in SL_2(C)
摘要：
本文在任意有限生成群G上刻划了满足恒等式f（xy）+f（xy^{-1}）=2f（x）+2f（y）的映射G->C的空间.已知（但不是众所周知的）这些函数对应于SL 2（C）中G的特征标簇的平凡特征标处的Zapriki-切向量。我们研究了使平凡特征标沿f所给方向变形的障碍。证明了当dim H_1（G，C）<2时平凡特征标是特征标簇的光滑点，当dim H_1（G，C）>2时平凡特征标不是光滑点.
英文摘要：
We describe on any finitely generated group G the space of maps G->C which satisfy the parallelogram identity, f(xy)+f(xy^{-1})=2f(x)+2f(y). It is known (but not well-known) that these functions correspond to Zariski-tangent vectors at the trivial character of the character variety of G in SL_2(C). We study the obstructions for deforming the trivial character in the direction given by f. Along the way, we show that the trivial character is a smooth point of the character variety if dim H_1(G,C)<2 and not a smooth point if dim H_1(G,C)>2.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
