Universal enveloping H-pseudoalgebras of DGP pseudoalgebras

2025/05/13 by Chen, Ying, Lü, Jiafeng, Wei, Jiaqun
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.08494

Abstract

The notions of Poisson H-pseudoalgebras are generalizations of Poisson algebras in a pseudotensor category M^∗(H). This paper introduces an analogue of Poisson-Ore extension in Poisson H-pseudoalgebras. Poisson H-pseudoalgebras with the differential graded setting induces the notions of differential graded Poisson H-pseudoalgebras (DGP pseudoalgebras, for short). The DGP pseudoalgebra with some compatibility conditions is proved to be closed under tensor product. Furthermore, the universal enveloping H-pseudoalgebras of DGP pseudoalgebras are constructed by a P-triple. A unique differential graded pseudoalgebra homomorphism between a universal enveloping H-pseudoalgebra of a DGP pseudoalgebra and a P-triple of a DGP pseudoalgebra is obtained.

Citations

• Enveloping algebras of double Poisson-Ore extensions
• PBW-basis for universal enveloping algebras of differential graded Poisson algebras
• Ore extensions and Poisson algebras
• Theory of Non-Commutative Polynomials

Related

• The structures on the universal enveloping algebras of differential graded Poisson Hopf algebras
• Universal Enveloping Algebras of Poisson Superalgebras
• Poisson Pseudoalgebras
• PBW-basis for universal enveloping algebras of differential graded Poisson algebras
• Universal enveloping algebras of weighted differential Poisson algebras