Results 191 to 200 of about 59,230 (210)

Down-Up Algebras From Trees

Communications in Algebra, 2006
It is shown that the global dimension of any n-ary down-up algebra A n  = A(n,α, β,γ) is less than or equal to n + 2, and when γ i  = 0 for all i (A n is graded by total degree in the generators), then the global dimension of A n is n + 2. Furthermore, a sufficient condition for A n to be prime is given; when γ i  = 0 for all i this condition is also ...
Ellen Kirkman, James Kuzmanovich
openaire   +3 more sources

Homogenized Down-Up Algebras

Communications in Algebra, 2003
This paper studies two homogenizations of the down-up algebras introduced in Benkart and Roby (Benkart, G., Roby, T. (1998). Down-up Algebras. J. Algebra 209:305–344).
Thomas Cassidy
openaire   +3 more sources

PRIMITIVE IDEALS OF NON-NOETHERIAN DOWN-UP ALGEBRAS

Communications in Algebra, 2005
ABSTRACT We identify the primitive ideals of non-Noetherian down-up algebras by determining specific elements that generate them. Primitive ideals of Noetherian down-up algebras have been previously identified, so in this work we complete the classification of primitive ideals in down-up algebras over ℂ.
Iwan Praton, Stephen May
openaire   +3 more sources

Simple Modules and Primitive Ideals of Non-Noetherian Generalized Down-Up Algebras

Communications in Algebra, 2009
Generalized down-up algebras were first introduced in Cassidy and Shelton (2004). Their simple weight modules were classified in Cassidy and Shelton (2004) in the noetherian case, and in Praton (2007) in the non-noetherian case. Here we concentrate on non-noetherian down-up algebras. We show that almost all simple modules are weight modules.
openaire   +3 more sources

Non-noetherian down-up algebras

Communications in Algebra, 2000
Ellen Kirkman, James Kuzmanovich
openaire   +3 more sources

Primitivity of Noetherian Down-Up Algebras

Communications in Algebra, 2000
Ellen Kirkman, James Kuzmanovich
openaire   +3 more sources

Primitive Ideals of Noetherian Down-Up Algebras

Communications in Algebra, 2004
openaire   +3 more sources

Simple Weight Modules of Non-Noetherian Generalized Down-Up Algebras

Communications in Algebra, 2006
openaire   +3 more sources

A Hopf structure for down-up algebras

Mathematische Zeitschrift, 2001
Down-up algebras were introduced by \textit{G. Benkart} and \textit{T. Roby} [J. Algebra 209, No. 1, 305-344 (1998; Zbl 0922.17006)] as a generalization of the algebra determined by the down and up operators on a partially ordered set. Specifically, if \(K\) is a field, then \(A=A(\alpha,\beta,\gamma)\) is the \(K\)-algebra generated by the elements ...
Benkart, Georgia, Witherspoon, Sarah
openaire   +2 more sources

Calabi–Yau properties of nontrivial Noetherian DG down-up algebras

Journal of Algebra and Its Applications, 2018
In this paper, we introduce and study differential graded (DG) down–up algebras. In brief, a DG down–up algebra [Formula: see text] is a connected cochain DG algebra such that its underlying graded algebra [Formula: see text] is a graded down–up algebra. We describe all possible differential structures on Noetherian DG down–up algebras.
Mao, X.-F., He, J.-W., Liu, M., Xie, J.-F.   +3 more
openaire   +2 more sources