Prime Ideals in Enveloping Rings
Copyright policy )Prime Ideals in Enveloping Rings
Let L L be a Lie algebra over the field K K of characteristic 0 0 and let U ( L ) U(L) denote its universal enveloping algebra. If R R is a K K -algebra and L L acts on R R as derivations, then there is a natural ring generated by R R and U ( L ) U(L) which is denoted by R # U ( L ) R\# U(L) and called the smash product of R R by U ( L ) U(L) . The aim of this paper is to describe the prime ideals of this algebra when it is Noetherian. Specifically we show that there exists a twisted enveloping algebra U ( X ) U(X) on which L L acts and a precisely defined one-to-one correspondence between the primes P P of R # U ( L ) R\#U(L) with P ∩ R = 0 P \cap R = 0 and the L L -stable primes of U ( X ) U(X) . Here X X is a Lie algebra over some field C ⊇ K C \supseteq K .
Prime and semiprime associative rings, Noetherian rings and modules (associative rings and algebras), Lie algebra, enveloping algebra, twisted enveloping algebra, crossed product, Universal enveloping (super)algebras, symmetric Martindale ring of quotients, smash product, prime length, Automorphisms, derivations, other operators for Lie algebras and super algebras, derivations, prime ideals, incomparability, Lie ideals, Poincaré-Birkhoff-Witt theorem, semiprimitive ring, prime ring, right Noetherian, Rings with involution; Lie, Jordan and other nonassociative structures, Simple and semisimple modules, primitive rings and ideals in associative algebras, Modules, bimodules and ideals in associative algebras, Lie ring, extended centroid
Prime and semiprime associative rings, Noetherian rings and modules (associative rings and algebras), Lie algebra, enveloping algebra, twisted enveloping algebra, crossed product, Universal enveloping (super)algebras, symmetric Martindale ring of quotients, smash product, prime length, Automorphisms, derivations, other operators for Lie algebras and super algebras, derivations, prime ideals, incomparability, Lie ideals, Poincaré-Birkhoff-Witt theorem, semiprimitive ring, prime ring, right Noetherian, Rings with involution; Lie, Jordan and other nonassociative structures, Simple and semisimple modules, primitive rings and ideals in associative algebras, Modules, bimodules and ideals in associative algebras, Lie ring, extended centroid
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