On Z-graded associative algebras and their N-graded modules
| dc.creator | Li, Haisheng | |
| dc.creator | Wang, Shuqin | |
| dc.date | 1999-03-19 | |
| dc.date.accessioned | 2026-07-07T05:28:23Z | |
| dc.date.available | 2026-07-07T05:28:23Z | |
| dc.description | Let $A$ be a $Z$-graded associative algebra and let $ρ$ be an irreducible $N$-graded representation of $A$ on $W$ with finite-dimensional homogeneous subspaces. Then it is proved that $ρ(\tilde{A})=gl_{J}(W)$, where $\tilde{A}$ is the completion of $A$ with respect to a certain topology and $gl_{J}(W)$ is the subalgebra of $\End W$, generated by homogeneous endomorphisms. It is also proved that an $N$-graded vector space $W$ with finite-dimensional homogeneous spaces is the only continuous irreducible $N$-graded $gl_{J}(W)$-module up to equivalence, where $gl_{J}(W)$ is considered as a topological algebra in a certain natural way, and that any continuous $N$-graded $gl_{J}(W)$-module is a direct sum of some copies of $W$. A duality for certain subalgebras of $gl_{J}(W)$ is also obtained. | |
| dc.description | AMS-LaTex 1.2, 17 pp, to appear in the Proceedings of the Conference at NCSU, Raleigh, May 1998 | |
| dc.identifier | https://arxiv.org/abs/math/9903117 | |
| dc.identifier | http://arxiv.org/abs/math/9903117 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78241 | |
| dc.subject | Quantum Algebra | |
| dc.title | On Z-graded associative algebras and their N-graded modules | |
| dc.type | text |