Endomorphisms of right ideals of the Weyl algebra
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- by J. T. Stafford PDF
- Trans. Amer. Math. Soc. 299 (1987), 623-639 Request permission
Abstract:
Let $A = A(k)$ be the first Weyl algebra over an infinite field $k$, let $P$ be any noncyclic, projective right ideal of $A$ and set $S = \operatorname {End} (P)$. We prove that, as $k$-algebras, $S\not \cong A$. In contrast, there exists a noncyclic, projective right ideal $Q$ of $S$ such that $S \cong \operatorname {End} (Q)$. Thus, despite the fact that they are Morita equivalent, $S$ and $A$ have surprisingly different properties. For example, under the canonical maps, ${\operatorname {Aut} _k}(A) \cong {\operatorname {Pic} _k}(A) \cong {\operatorname {Pic} _k}(S)$. In contrast, ${\operatorname {Aut} _k}(S)$ has infinite index in ${\operatorname {Pic} _k}(S)$.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 299 (1987), 623-639
- MSC: Primary 16A89; Secondary 16A19, 16A33, 16A65, 17B35
- DOI: https://doi.org/10.1090/S0002-9947-1987-0869225-3
- MathSciNet review: 869225