2024/11/05 by Chen, Ying, Kang, Chuangchuang, Lü, Jiafeng
#16S10 #16S30 #17B35 #17B63 #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2411.03046
The λ-differential operators and modified λ-differential operators are generalizations of classical differential operators. This paper introduces the notions of λ-differential Poisson (λ-DP for short) algebras and modified λ-differential Poisson (λ-mDP for short) algebras as generalizations of differential Poisson algebras. The λ-DP algebra is proved to be closed under tensor product, and a λ-DP algebra structure is provided on the cohomology algebra of the λ-DP algebra. These conclusions are also applied to λ-mDP algebras and their modules. Finally, the universal enveloping algebras of λ-DP algebras are generalized by constructing a P-triple. Three isomorphisms among opposite algebras, tensor algebras and the universal enveloping algebras of λ-DP algebras are obtained.