The cohomology of the nilCoxeter algebra
Abstract
The nilCoxeter algebra $\mathcal{N}S_n$ of the symmetric group $S_n$ is the algebra over $\mathbb{Z}$ with generators $Y_i$ ($1\leqslant i\leqslant n-1$), satisfying the braid relations $Y_iY_{i+1}Y_i=Y_{i+1}Y_iY_{i+1}$, $Y_iY_j=Y_jY_i$ ($|j-i|\geqslant 2$), together with the relations $Y_i^2=0$. We describe an explicit presentation for the cohomology ring $Z\cong\mathsf{Ext}^*_{\mathcal{N}S_n}(\mathbb{Z},\mathbb{Z})$, with $n-i$ new generators in degree $i$ for $0< i
Fields of Study & Subjects
Advanced Topics in Algebra
Advanced Operator Algebra Research
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Homology Homotopy and Applications
- Publisher
- International Press of Boston
- Volume
- 28
- Issue
- 1
- Pages
- 149–173
- Publication date
- 1 January 2026
- Language
- EN