A POINCARÉ-BIRKHOFF-WITT THEOREM FOR POISSON ENVELOPING ALGEBRAS

DOI10.1081/AGB-120014673zbMath1023.17014MaRDI QIDQ4799327

Yongyeon Shin, Sei-Qwon Oh, Chun-Gil Park

Publication date: 12 November 2003

Published in: Communications in Algebra (Search for Journal in Brave)

zbMATH Keywords

Poisson bracketsenveloping algebrasPoisson algebraGröbner-Shirshov basisPoincaré-Birkhoff-Witt theoremPoisson modulesymplectic ideal

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Universal enveloping (super)algebras (17B35) Poisson algebras (17B63) Other classes of modules and ideals in associative algebras (16D80) Universal enveloping algebras of Lie algebras (16S30) Nonassociative algebras satisfying other identities (17A30)

Related Items

Poisson enveloping algebras and the Poincaré-Birkhoff-Witt theorem, Free generic Poisson fields and algebras, Poincaré–Birkhoff–Witt theorem for Poisson enveloping algebra, The structures on the universal enveloping algebras of differential graded Poisson Hopf algebras, Universal Poisson Envelope for Binary-Lie Algebras, The \(N\)-isometric isomorphisms in linear \(N\)-normed \(C^{\ast}\)-algebras, Gelfand–Kirillov Dimension of Algebras with a Locally Finite and Multiparameter Indexed Filtration, Universal enveloping algebras and universal derivations of Poisson algebras, Quantum and Poisson structures of multi-parameter symplectic and Euclidean spaces, Approximately linear mappings in Banach modules over a \(C^*\)-algebra, Universal enveloping algebras of Poisson Hopf algebras, PBW-basis for universal enveloping algebras of differential graded Poisson algebras, Realization of Poisson enveloping algebra, Enveloping algebras of double Poisson-Ore extensions, STABILITY OF HOMOMORPHISMS IN BANACH MODULES OVER A C^*-ALGEBRA ASSOCIATED WITH A GENERALIZED JENSEN TYPE MAPPING AND APPLICATIONS, Unnamed Item, Poisson enveloping algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Primitive ideals of \({\mathbf C}_ q[SL(3)\)]
• Primitive ideals of \(\mathbb{C}_ q[SL(n)\)]
• Gröbner-Shirshov bases for irreducible \(sl_{n+1}\)-modules
• Primitive and Poisson spectra of twists of polynomial rings
• Symplectic ideals of poisson algebras and the poisson structure associated to quantum matrices
• Poisson enveloping algebras