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Unravelling the Holomorphic Twist: Central Charges. [PDF]
Commun Math PhysBomans P, Wu J.
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Representation theory of coherent photons and application to CNOT operation for spin and orbital angular momentum. [PDF]
Sci RepSaito S.
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Decompositions of Hyperbolic Kac-Moody Algebras with Respect to Imaginary Root Groups. [PDF]
Commun Math PhysFeingold AJ, Kleinschmidt A, Nicolai H.
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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
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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
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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).
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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).
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A Hopf structure for down-up algebras
Mathematische Zeitschrift, 2001Down-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
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PRIMITIVE IDEALS OF NON-NOETHERIAN DOWN-UP ALGEBRAS
Communications in Algebra, 2005ABSTRACT 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
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Calabi–Yau properties of nontrivial Noetherian DG down-up algebras
Journal of Algebra and Its Applications, 2018In 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. +3 more
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CENTERS OF DOWN-UP ALGEBRAS OVER FIELDS OF PRIME CHARACTERISTIC
Communications in Algebra, 2002ABSTRACT We consider down-up algebras as defined by Benkart and Roby over ground fields of characteristic p and find the centers of those algebras. The method used here also illustrates a way of computing the center of a down-up over a field of characteristic 0 different from the ones used by Zhao [5] and by Kulkarni [3].
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