Published in Annals of Global Analysis and Geometry
We describe the generalized Kuranishi spaces of solvmanifolds with left-invariant complex structures. By using such description, we study the stability of left-invariantness of deformed generalized complex structures and smoothness of generalized Kuranishi spaces on certain classes of solvmanifolds. We also give explicit finite-dimensional cochain ...
Published in Journal of Pseudo-Differential Operators and Applications
We consider the action of the Lie algebra aff(1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {aff}(1)$$\end{document}, by the Lie derivative on the space o...
Published in Acta Mathematica Hungarica
Over the (1,N)-dimensional real superspace, N≧3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${N \geqq 3}$$\end{document}, we study non-trivial deformations of the nat...
Published in Open Mathematics
We introduce a notion of Jacobi-Bernoulli cohomology associated to a semi-simplicial Lie algebra (SELA). For an algebraic scheme X over ℂ, we construct a tangent SELA J X and show that the Jacobi-Bernoulli cohomology of J X is related to infinitesimal deformations of X.
Published in Acta Mathematica Hungarica
We consider the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak{sl}\, (2)$\end{document}-module structure on the spaces of symbols of differential operators ac...
Published in Acta Applicandae Mathematicae
A general theory of the Frölicher–Nijenhuis and Schouten–Nijenhuis brackets in the category of modules over a commutative algebra is described. Some related structures and (co)homology invariants are discussed, as well as applications to geometry.
