Radicals of crossed products of enveloping algebras |
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| Authors: | Jeffrey Bergen S Montgomery D S Passman |
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| Institution: | (1) Mathematics Department, De Paul University, 60604 Chicago, IL, USA;(2) Mathematics Department, University of Southern California, 90089 Los Angeles, CA, USA;(3) Mathematics Department, University of Wisconsin — Madison, 53706 Madison, WI, USA |
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| Abstract: | LetL be a Lie algebra over a fieldK which acts asK-derivations on aK-algebraR. Then this action determines a crossed productR *U(L) whereU(L) is the enveloping algebra ofL. The goal of this paper is to describe the Jacobson radical ofR * U(L) forL≠0. We are most successful whenR is a p.i. algebra or Noetherian. In more general situations we at least obtain upper and lower bounds forJ(R * U(L)) which are ideals extended fromR. Furthermore, we offer an interesting example in all characteristics of a commutativeK-algebraC which admits a derivationδ such thatC isδ-prime but not semiprime.
Partially supported by N.S.F. Grant No. DMS 85-00959 and by a Guggenheim Memorial Foundation Fellowship.
Partially supported by N.S.F. Grant No. MCS 82-19678. |
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