Abstract
4.1.1. Completions. Let (U ⊗ U)^ be the completion of the vector space U ⊗ U with respect to the descending sequence of vector spaces
for N = 1,2,…. Note that each H N is a left ideal in U ⊗ U; moreover, for any u∈U ⊗ U, we can find r ≥ 0 such that H N + r u ⊂ H N for all N ≥ 0. It follows that the Q(v)-algebra structure on U ⊗ U extends by continuity to a Q(v)-algebra structure on (U ⊗ U)^. We have an obvious imbedding of algebras U ⊗ U→(U ⊗ U)^.
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Lusztig, G. (2010). The Quasi-\(\mathcal{R}\)-Matrix. In: Introduction to Quantum Groups. Modern Birkhäuser Classics. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4717-9_4
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DOI: https://doi.org/10.1007/978-0-8176-4717-9_4
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