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The Extension Group of the Simple Modules Over the First Weyl Algebra
Author(s) -
Bavula V. V.
Publication year - 2000
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609399006608
Subject(s) - mathematics , simple (philosophy) , extension (predicate logic) , simple module , weyl algebra , zero (linguistics) , algebra over a field , weyl group , pure mathematics , mathematics subject classification , verma module , field (mathematics) , lie algebra , computer science , linguistics , philosophy , epistemology , programming language
The aim of this paper is to prove that for certain generalized Weyl algebras A (including the first Weyl algebra A 1 over a field of characteristic zero) and for every simple left (right) A ‐module M , there are infinitely many non‐isomorphic simple left (right) A ‐modules { N i } such that E x t A 1 ( M , N i ) ≠ 0 (respectivelyExt A 1 ( N i , M ) ≠ 0 ). 1991 Mathematics Subject Classification 18G15, 16G.