ψ^3 as an upper triangular matrix

Upper triangular matrices and operations in odd primary connective K-theory

We prove analogues for odd primes of results of Snaith and Barker-Snaith. Let l denote the p-complete connective Adams summand and consider the group of left l-module automorphisms of l smash l in the stable homotopy category which induce the identity on mod p homology. We prove a group isomorphism between this group and a certain group of infinite invertible upper triangular matrices with entries in the p-adic integers. We determine information about the matrix corresponding to the automorphism 1 smash Psi^q, where Psi^q is the Adams operation and q is an integer which generates the p-adic un…

通过lax极限得到上三角环谱的导出等价

Derived equivalences of upper-triangular ring spectra via lax limits

本文将Ladkani关于上三角矩阵环的导出等价定理推广至环谱，并同时推广了Maycock对微分分次代数的类似结果。

上三角矩阵的交换概形与表示同调

Commuting Schemes of Upper Triangular Matrices and Representation Homology

本研究建立了与上三角幂幺矩阵群概形$U_n$相关的高亏格广义交换概形$C_g(U_n)$和黎曼曲面的$U_n$系数表示同调的联系，并给出了判定$C(U_n)$是否为完全交的数值准则。

关于平方零上三角矩阵猜想的秩8情况

The rank 8 case of a conjecture on square-zero upper triangular matrices

本文研究了平方零上三角矩阵猜想的秩8情况，证明在不考虑特征限制下该猜想成立，并进一步验证了某些拓扑空间上2-群作用的自由性。

Characteristic classes of Borel orbits of square-zero upper-triangular matrices

Anna Melnikov provided a parametrization of Borel orbits in the affine variety of square-zero $n \times n$ matrices by the set of involutions in the symmetric group. A related combinatorics leads to a construction a Bott-Samelson type resolution of the orbit closures. This allows to compute cohomological and K-theoretic invariants of the orbits: fundamental classes, Chern-Schwartz-MacPherson classes and motivic Chern classes in torus-equivariant theories. The formulas are given in terms of Demazure-Lusztig operations. The case of square-zero upper-triangular matrices is reach enough to include…