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From Poisson algebras to Gerstenhaber algebras

Yvette Kosmann-Schwarzbach (1996)

Annales de l'institut Fourier

Constructing an even Poisson algebra from a Gerstenhaber algebra by means of an odd derivation of square 0 is shown to be possible in the category of Loday algebras (algebras with a non-skew-symmetric bracket, generalizing the Lie algebras, heretofore called Leibniz algebras in the literature). Such “derived brackets” give rise to Lie brackets on certain quotient spaces, and also on certain Abelian subalgebras. The construction of these derived brackets explains the origin of the Lie bracket on...

H¹ and BMO for certain locally doubling metric measure spaces of finite measure

Andrea Carbonaro, Giancarlo Mauceri, Stefano Meda (2010)

Colloquium Mathematicae

In a previous paper the authors developed an H¹-BMO theory for unbounded metric measure spaces (M,ρ,μ) of infinite measure that are locally doubling and satisfy two geometric properties, called “approximate midpoint” property and “isoperimetric” property. In this paper we develop a similar theory for spaces of finite measure. We prove that all the results that hold in the infinite measure case have their counterparts in the finite measure case. Finally, we show that the theory applies to a class...

On topological degree and Poincaré duality

Franco Cardin (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this Note we investigate about some relations between Poincaré dual and other topological objects, such as intersection index, topological degree, and Maslov index of Lagrangian submanifolds. A simple proof of the Poincaré-Hopf theorem is recalled. The Lagrangian submanifolds are the geometrical, multi-valued, solutions of physical problems of evolution governed by Hamilton-Jacobi equations: the computation of the algebraic number of the branches is showed to be performed by using Poincaré dual....

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