Abstract
In this paper, we study the twisted Poisson homology of truncated polynomials algebra A in four variables, and we calculate exactly the dimension of i-th (i = 1, 2, 3, 4) twisted Poisson homology group over A by the induction on the length. The calculation methods provided in this paper can also solve truncated polynomials algebra in a few variables.
Highlights
We study the twisted Poisson homology of truncated polynomials algebra A in four variables, and we calculate exactly the dimension of i-th (i = 1, 2, 3, 4) twisted Poisson homology group over A by the induction on the length
From the above Theorem, the dimension of Poisson cohomology space is determined by calculating twisted Poisson homology
When we calculate the 1-th twisted Poisson homology group, we have found that each element of length 0 in AD ⊗ Ω2 ( A)
Summary
We study the twisted Poisson homology of truncated polynomials algebra A in four variables, and we calculate exactly the dimension of i-th (i = 1, 2, 3, 4) twisted Poisson homology group over A by the induction on the length. Twisted Poisson Homology, Poisson Algebra, (Twisted) Poisson Module [2]) studied the Poisson (co)homology of the algebra of the truncated polynomial in two variables and established a duality between the two. Let S be a Frobenius Poisson algebra.
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