Amalgams of Weyl algebras and theA (V, δ, Γ) conjecture
Tóm tắt
We prove a long standing conjecture ([5, Conjecture 5.6]) concerning the algebrasA (V, δ, Γ). Namely, two such algebrasA (V, δ, Γ),A (W, ε, Ω) are isomorphic if and only if there is an isomorphism between the ‘triples’ (V, δ, Γ), (W, ε, Ω) from which they are constructed. As a consequence, to each primitive ideal in the enveloping algebra of a solvable Lie algebra there is associated a unique (V, δ, Γ).
Tài liệu tham khảo
Borho, W., Gabriel, P., Rentschler, R.: Primideale in Einhüllenden auflösbarer Lie Algebren, (Lect. Notes Math., Vol. 357). Berlin Heidelberg New York: Springer 1973
Dixmier, H.: Enveloping algebras. North-Holland 1977
McConnell, J.C.: A note on the Weyl algebraA n . Proc. London Math. Soc.28, 89–98 (1974)
McConnell, J.C.: Representations of solvable Lie algebras and the Gelfand-Kirillov conjecture. Proc. London Math. Soc.29, 453–484 (1974)
McConnell, J.C.: Representations of solvable Lie algebras II: Twisted group rings. Ann. Sci. Éc. Norm. Super., IV. Ser.8, 157–178 (1975)
McConnell, J.C.: Representations of solvable Lie algebras III: Cancellation theorems. J. Algebra44, 262–270 (1977)
McConnell, J.C., Robson, J.C.: Noncommutative Noetherian rings. Chichester and New York: J. Wiley 1987
Tauvel, P.: Sur les quotients premiers de l'algèbre enveloppante d'une algèbre de Lie résoluble. Bull. Soc. Math. France106, 177–205 (1978)
Tauvel, P.: Sur les quotients premiers de l'algèbre enveloppante d'une algèbre de Lie résoluble II. Ann. Fac. Sci. Toulouse, V. Ser. Math.1, 257–267 (1979)
Tauvel, P.: Sur la dimension de Gelfand-Kirillov. Commun. Algebra10, 939–964 (1982)