The Extension Group of the Simple Modules Over the First Weyl Algebra | Zendy

Bavula V. V. | Zendy

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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.

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