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On Z-graded associative algebras and their N-graded modules | | Haisheng Li
; Shuqin Wang
; | | Date: |
19 Mar 1999 | | Subject: | Quantum Algebra | math.QA | | Abstract: | Let $A$ be a $Z$-graded associative algebra and let $
ho$ be an irreducible $N$-graded representation of $A$ on $W$ with finite-dimensional homogeneous subspaces. Then it is proved that $
ho( ilde{A})=gl_{J}(W)$, where $ ilde{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. | | Source: | arXiv, math.QA/9903117 | | Services: | Forum | Review | PDF | Favorites | |
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