Jonas T. Hartwig
Multiparameter Twisted Weyl Algebras.
Wed, 03/30/2011 - 15:01 — SomNambulAuthors: Jonas T. Hartwig, Vyacheslav Futorny
Subjects: Quantum Algebra
AbstractWe introduce a new family of twisted generalized Weyl algebras, called
multiparameter twisted Weyl algebras, for which we parametrize all simple
quotients of a certain kind. Both Jordan's simple localization of the
multiparameter quantized Weyl algebra and Hayashi's q-analog of the Weyl
algebra are special cases of this construction. We classify all simple weight
modules over any multiparameter twisted Weyl algebra.- Read more
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On the Consistency of Twisted Generalized Weyl Algebras.
Thu, 03/24/2011 - 16:01 — SomNambulAuthors: Jonas T. Hartwig, Vyacheslav Futorny
Subjects: Rings and Algebras
AbstractA twisted generalized Weyl algebra A of degree n depends on a base algebra R,
n commuting automorphisms s_i of R, n central elements t_i of R and on some
additional scalar parameters. In a paper by V.Mazorchuk and L.Turowska (1999)
it is claimed that certain consistency conditions for s_i and t_i are
sufficient for the algebra to be nontrivial. However, in this paper we give an
example which shows that this is false.Twisted generalized Weyl algebras, polynomial Cartan matrices and Serre-type relations.
Mon, 08/17/2009 - 18:30 — SomNambulAuthors: Jonas T. Hartwig
Subjects: Rings and Algebras
AbstractTwisted generalized Weyl algebras (TGWAs) are defined as the quotient of a
certain graded algebra by the maximal graded ideal I with trivial zero
component, analogous to how Kac-Moody algebras can be defined. In this paper we
introduce the class of locally finite TGWAs, and show that one can associate to
such an algebra a polynomial Cartan matrix (a notion extending the usual
generalized Cartan matrices appearing in Kac-Moody algebra theory) and that the
corresponding generalized Serre relations hold in the TGWA.
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