8 citations · 30 across the 15 of their papers we have counts for
15 papers
Super homology groups of differential forms and vector fields on Euclidean line
Kentaro Mikami, Tadayoshi Mizutani
The arXiv:2105.09738 claims several stuffs. In particular, we recall the following two. (1) Vector fields and differential forms become a Lie superalgebra structure for each manifo…
Poisson-like cohomologies associated with some Lie superalgebras
Kentaro Mikami, Tadayoshi Mizutani, Hajime Sato
The concept of Poisson cohomology groups associated with Poisson manifolds is a part of the theory of Lie superalgebras of vector fields. Therefore, we abstracted them as Poisson-l…
Application of superalgebra homology groups to distinguish Engel-like structures
Kentaro Mikami, Tadayoshi Mizutani, Hajime Sato
There are three kinds of Lie superalgebras for each differentiable manifold. In this note, we shall show an application of the homology groups of those superalgebras in order to cl…
Deformed super brackets on forms of a manifold
Kentaro Mikami, Tadayoshi Mizutani
Given a manifold, we have a super bracket on the graded algebra of differential forms by {A,B} = (-1)^{a} d(A \wedge B). We study when {A,B}_{t} = (-1)^{a} d(A \wedge B) + F(a,b) A…
Superalgebra structure on differential forms of manifold
Kentaro Mikami, Tadayoshi Mizutani
As an analogy of superalgebra of multivector fields with the Schounte bracket, we introduce a non-trivial superbracket on differential forms of manifold. We show properties of this…
Super homologies associated with low dimensional Lie algebras
Kentaro Mikami, Tadayoshi Mizutani
A Poisson structure on a manifold is characterized by the Schouten bracket. The graded algebra of the tangent bundle with the Schouten bracket is a prototype of Lie superalgebra. T…
The second Betti number of doubly weighted homology groups of some pre Lie superalgebra
Kentaro Mikami, Tadayoshi Mizutani
We already showed that Betti numbers are all zero when w is not equal to h for (w,h)-doubly weighted homology groups of some special pre Lie superalgebra and showed the first Betti…
Euler number and Betti numbers of homology groups of pre Lie superalgebra
Kentaro Mikami, Tadayoshi Mizutani
First we recall homology groups of prer Lie superalgebras. Then introducing double weighted chain spaces, we deal with pre Lie superalgebra of multi-vector fields with polynomial c…
First Betti number of weighted homology group of Hamiltonian vector fields on symplectic tori
Hiroki Kodama, Kentaro Mikami, Tadaysshi Mizutani
Like (co)homology group theory of formal Hamiltonian vector fields on symplectic vector spaces, we try studying homology group theory on symplecit tori introducing the notion of we…
Cohomology groups of homogeneous Poisson structures
Kentaro Mikami, Tadayoshi Mizutani
We generalize the notion of weight for Gelfan'd-Fuks cohomology theory of symplectic vector spaces to the homogeneous Poisson vector spaces, and try some combinatorial approach to…
An affirmative answer to a conjecture for Metoki class
Kentaro Mikami
In "The {G}el'fand-{K}alinin-{F}uks class and characteristic classes of transversely symplectic foliations" arXiv:0910.3414, Kotschick and Morita showed that the Gel'fand-Kalinin-F…
Another proof to Kotschick-Morita's Theorem of Kontsevich homomorphism
Kentaro Mikami
In \cite{KOT:MORITA}, Kotschick and Morita showed that the Gel'fand-Kalinin-Fuks class in $\ds \HGF{7}{2}{}{8}$ is decomposed as a product of some leaf cohomology class…
The relative Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields on 6-dimensional plane
Kentaro Mikami
Using Crystal basis theory, we study the relative Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields on 6-dimensional plane with weight =2,4,6.
Lower weight Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields on R^4
Kentaro Mikami, Yasuharu Nakae
In this paper, we investigate the relative Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields on R^4. In the case of formal Hamiltonian vector fields o…
Higher weight Gel'fand-Kalinin-Fuks classes of formal Hamiltonian vector fields of symplectic R^2
Kentaro Mikami, Hiroki Kodama, Yasuharu Nakae
In "The Gel'fand-Kalinin-Fuks class and characteristic classes of transversely symplectic foliations", arXiv:0910.3414, (October 2009) by D.Kotschick and S.Morita, the relative Gel…