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Article: Noetherian downup algebras
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ABSTRACT: Downup algebras A = A(α, β, γ) were introduced by G. Benkart and T. Roby to better understand the structure of certain posets. In this paper, we prove that β = 0 is equivalent to A being right (or left) Noetherian, and also to A being a domain. Furthermore, when this occurs, we show that A is Auslanderregular and has global dimension 3.Proceedings of the American Mathematical Society 01/2000; 28(11). · 0.68 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Let g be the Lie superalgebra osp(1; 2r). We show that there is a surjective homomorphism from U(g )t o the r th Weyl algebra Ar ,a nd we use this to construct an analog of the Joseph ideal. We also obtain a decomposition of the adjoint representation of g on Ar and use this to show that if Ar is made into a Lie superalgebra using its natural Z2grading, then Ar = k (Ar;Ar). In addition, we show that if (Ar;Ar )a nd ( A s;As )a re isomorphic as Lie superalgebras, then r = s. This answers a question of S. Montgomery.Proceedings of the American Mathematical Society 10/1999; 127(10). DOI:10.1090/S000299399904976X · 0.68 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A class of algebras called down–up algebras was introduced by G. Benkart and T. Roby (1998, J. Algebra209, 305–344). We classify the finite dimensional simple modules over Noetherian down–up algebras and show that in some cases every finite dimensional module is semisimple. We also study the question of when two down–up algebras are isomorphic.Journal of Algebra 04/1999; 228(1228):286310. DOI:10.1006/jabr.1999.8263 · 0.60 Impact Factor 
Article: Crystal Bases for U q ( osp(1, 2 r))
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ABSTRACT: We construct Z2graded crystal bases for the quantized universal enveloping algebra of the Lie superalgebraosp(1,2r). We show that, like the crystal bases in the Lie algebra case, these crystal bases carry a remarkable combinatorial structure.Journal of Algebra 12/1998; 210(2):514534. DOI:10.1006/jabr.1998.7591 · 0.60 Impact Factor 
Article: Crystal Bases for Uq(osp(1, 2r))
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ABSTRACT: We construct 2graded crystal bases for the quantized universal enveloping algebra of the Lie superalgebra osp(1, 2r). We show that, like the crystal bases in the Lie algebra case, these crystal bases carry a remarkable combinatorial structure. Copyright 1998 Academic Press.Journal of Algebra 11/1998; 210(2):514534. · 0.60 Impact Factor 
Article: Invariants under tori of rings of differential operators and related topics / Ian M. Musson
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ABSTRACT: November 1998, volume 136, number 650 (fifth of 6 numbers) Incluye bibliografíaMemoirs of the American Mathematical Society 01/1998; DOI:10.1090/memo/0650 · 1.73 Impact Factor  Journal of Algebra 07/1997; 193(1):75101. DOI:10.1006/jabr.1996.7000 · 0.60 Impact Factor
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ABSTRACT: We describe the skew primitive elements in a multiparameter enveloping algebraU=U q,p −1 (g) and the links between cofinite maximal ideals in the corresponding quantum function algebra ℂ q [G]. These results are applied to determine the coradical filtration forU, and to obtain a moduli space for multiparameter Drinfeld doubles.Israel Journal of Mathematics 01/1997; 100(1):285308. DOI:10.1007/BF02773644 · 0.79 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Let g be the Lie superalgebra osp(1; 2r )a nd U ( g) the enveloping algebra of g. In this paper we obtain a description of the set of primitive ideals PrimU(g) as an ordered set. We also obtain the multiplicities of composition factors of Verma modules over U(g), and of simple highest weight modules forU(g )w hen regarded as a U(g0)module by restriction.Representation Theory of the American Mathematical Society 01/1997; DOI:10.1090/S1088416597000204 · 0.73 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Let A = A(p, λ) be the multiparameter deformation of the coordinate algebra of n × n matrices as described by Artin, et al. (1991). Let U be the quantum enveloping algebra which is associated to A, in the sense of Faddeev, Reshetikhin and Takhtadzhyan. We prove a PBW theorem for U and establish a presentation by generators and relations, when λ is not a root of unity. Our approach depends on a cocycle twisting method which reduces many arguments to the standard oneparameter deformation.Journal of Pure and Applied Algebra 03/1996; 107(23107):171191. DOI:10.1016/00224049(95)000623 · 0.47 Impact Factor  Proceedings of the American Mathematical Society 03/1995; 123(3):693693. DOI:10.1090/S00029939199512217276 · 0.68 Impact Factor
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ABSTRACT: If X is a toric variety we show that X is isomorphic to a quotient Y G where G is a torus acting on an affine space ks and Y is a Ginvariant open subset of ks. We also show that any ring of differential operators on X twisted by an invertible sheaf is a factor ring of the fixed ring D(Y)G by an ideal generated by central elements.Journal of Pure and Applied Algebra 08/1994; 95(3):303–315. DOI:10.1016/00224049(94)900647 · 0.47 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Descriptions of the complete sets of irreducible highestweight modules over complex classical simple Lie superalgebras are recorded. It is further shown that the finitedimensional irreducible modules over a (not necessarily classical simple) finitedimensional complex Lie superalgebra form a complete set if and only if the even part of the Lie superalgebra is reductive and the universal enveloping superalgebra is semiprime.Letters in Mathematical Physics 06/1994; 31(3):247253. DOI:10.1007/BF00761716 · 1.94 Impact Factor  Communications in Algebra 01/1994; 22(1212):46614692. DOI:10.1080/00927879408825095 · 0.39 Impact Factor
 Journal of Algebra 08/1993; 159(2):306331. DOI:10.1006/jabr.1993.1158 · 0.60 Impact Factor

Article: Malcevneumann group rings
Communications in Algebra 01/1993; 21(66):20652075. DOI:10.1080/00927879308824665 · 0.39 Impact Factor 
Article: A classification of primitive ideals in the enveloping algebra of a classical Lie superalgebra
Advances in Mathematics 02/1992; 91(2). DOI:10.1016/00018708(92)90018G · 1.29 Impact Factor  Pacific Journal of Mathematics 01/1991; DOI:10.2140/pjm.1991.147.269 · 0.43 Impact Factor
 Archiv der Mathematik 12/1990; 56(1):8695. DOI:10.1007/BF01190085 · 0.39 Impact Factor
 Journal of the London Mathematical Society 12/1990; DOI:10.1112/jlms/s242.3.401 · 0.82 Impact Factor
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