arXiv math/06011322006-01math.AGmath.AC

3 × 3幺模矩阵对的生成元、关系和对称性

Generators, Relations and Symmetries in Pairs of 3x3 Unimodular Matrices

Sean Lawton

备注：: 21 pages. This fourth version is the author's final version which includes new comments and some corrections
发表信息：: J. Algebra 313 (2007), no. 2, 782--801
DOI：: 10.1016/j.jalgebra.2007.01.003

摘要：

用F2表示两个字母的自由群，用R = Hom（F2，SL（3，C））表示F2的SL（3，C）-表示簇。R的坐标环上存在SL（3，C）-作用，且不变量子环的几何点是仿射簇X。我们确定了显式极小生成元和不变量子环的定义关系，并证明了X是C9映射到C8的6次超曲面。我们选择的发电机展示出（F2）对称性，允许一个简洁的定义关系的表达。

英文摘要：

Denote the free group on two letters by F2 and the SL(3,C)-representation variety of F2 by R = Hom(F2, SL(3,C)). There is a SL(3,C)-action on the coordinate ring of R, and the geometric points of the subring of invariants is an affine variety X. We determine explicit minimal generators and defining relations for the subring of invariants and show X is a degree 6 hyper-surface in C9 mapping onto C8. Our choice of generators exhibit Out(F2) symmetries which allow for a succinct expression of the defining relations.

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。