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Correspondence between maximal ideals in associative algebras and Lie algebras. (English) Zbl 0678.17005
Proc. Winter Sch. Geom. Phys., Srní/Czech. 1988, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 21, 343-347 (1989).
[For the entire collection see Zbl 0672.00006.]
The paper considers a commutative associative algebra A with a unit element over a field K of characteristic zero and a subalgebra \(L\subset Der(A)\) which is an A-submodule such that \(LA=A\). A natural bijection between the set of all maximal invariant ideals in A and the set of all maximal ideals in L is exhibited.
This result leads to the description of all maximal invariant ideals in the real algebra \(C^{\infty}(V)\), where V is a connected paracompact \(C^{\infty}\) manifold.
Reviewer: M.Modugno
MSC:
17B05 Structure theory for Lie algebras and superalgebras
16Dxx Modules, bimodules and ideals in associative algebras