\(gl(\lambda)\) and differential operators preserving polynomials

DOI10.1007/BF00116524zbMath0910.17009OpenAlexW2165932964MaRDI QIDQ1815382

Nico Van den Hijligenberg, Gerhard F. Post

Publication date: 20 April 1999

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00116524

zbMATH Keywords

Lie algebras of differential operatorsdeformationsuniversal enveloping algebrapolynomial differential operators\(gl(\lambda)\)\(sl_2(\mathbb{C})\)

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Lie algebras of vector fields and related (super) algebras (17B66) Cohomology of Lie (super)algebras (17B56)

Related Items (7)

The celestial chiral algebra of self-dual gravity on Eguchi-Hanson space ⋮ New realizations of deformed double current algebras and Deligne categories ⋮ Integrability structures of the generalized Hunter-Saxton equation ⋮ Invariant modules and the reduction of nonlinear partial differential equations to dynamical systems ⋮ Polynomial forms for quantum elliptic Calogero-Moser Hamiltonians ⋮ The \(\mathcal N=1\) algebra \(\mathcal W_{\infty}[\mu\) and its truncations] ⋮ The Lie algebraic structure of differential operators admitting invariant spaces of polynomials

Cites Work

• Defining relations for Lie algebras of vector fields
• Quotients simples de l'algèbre enveloppante de \({\mathfrak sl}_2\)
• Lie algebras and polynomials in one variable
• Operator identities, representations of algebras and the problem of normal ordering
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