Grassmannians of two-sided vector spaces
| dc.creator | Nyman, A. | |
| dc.date | 2004-11-08 | |
| dc.date | 2009-02-27 | |
| dc.date.accessioned | 2026-07-07T12:47:14Z | |
| dc.date.available | 2026-07-07T12:47:14Z | |
| dc.description | Let $k \subset K$ be an extension of fields, and let $A \subset M_{n}(K)$ be a $k$-algebra. We study parameter spaces of $m$-dimensional subspaces of $K^{n}$ which are invariant under $A$. The space $\mathbb{F}_{A}(m,n)$, whose $R$-rational points are $A$-invariant, free rank $m$ summands of $R^{n}$, is well known. We construct a distinct parameter space, $\mathbb{G}_{A}(m,n)$, which is a fiber product of a Grassmannian and the projectivization of a vector space. We then study the intersection $\mathbb{F}_{A}(m,n) \cap \mathbb{G}_{A}(m,n)$, which we denote by $\mathbb{H}_{A}(m,n)$. Under suitable hypotheses on $A$, we construct affine open subschemes of $\mathbb{F}_{A}(m,n)$ and $\mathbb{H}_{A}(m,n)$ which cover their $K$-rational points. We conclude by using $\mathbb{F}_{A}(m,n)$, $\mathbb{G}_{A}(m,n)$, and $\mathbb{H}_{A}(m,n)$ to construct parameter spaces of two-sided subspaces of two-sided vector spaces. | |
| dc.description | 23 pages, changed content, minor errors corrected | |
| dc.identifier | https://arxiv.org/abs/math/0411172 | |
| dc.identifier | http://arxiv.org/abs/math/0411172 | |
| dc.identifier | Comm. Algebra, 35 (2007), 2208-2234 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221653 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Quantum Algebra | |
| dc.subject | 15A03, 14M15, 16D20 | |
| dc.title | Grassmannians of two-sided vector spaces | |
| dc.type | text |