Page 1 Next

Displaying 1 – 20 of 35

Showing per page

1 -cocycles on the group of contactomorphisms on the supercircle S 1 | 3 generalizing the Schwarzian derivative

Boujemaa Agrebaoui, Raja Hattab (2016)

Czechoslovak Mathematical Journal

The relative cohomology H diff 1 ( 𝕂 ( 1 | 3 ) , 𝔬𝔰𝔭 ( 2 , 3 ) ; 𝒟 λ , μ ( S 1 | 3 ) ) of the contact Lie superalgebra 𝕂 ( 1 | 3 ) with coefficients in the space of differential operators 𝒟 λ , μ ( S 1 | 3 ) acting on tensor densities on S 1 | 3 , is calculated in N. Ben Fraj, I. Laraied, S. Omri (2013) and the generating 1 -cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative 1 -cocycle s ( X f ) = D 1 D 2 D 3 ( f ) α 3 1 / 2 , X f 𝕂 ( 1 | 3 ) which is invariant with respect to the conformal subsuperalgebra 𝔬𝔰𝔭 ( 2 , 3 ) of 𝕂 ( 1 | 3 ) . In this work we study the supergroup case. We give an explicit construction of 1 -cocycles of the group...

A lossless reduction of geodesics on supermanifolds to non-graded differential geometry

Stéphane Garnier, Matthias Kalus (2014)

Archivum Mathematicum

Let = ( M , 𝒪 ) be a smooth supermanifold with connection and Batchelor model 𝒪 Γ Λ E * . From ( , ) we construct a connection on the total space of the vector bundle E M . This reduction of is well-defined independently of the isomorphism 𝒪 Γ Λ E * . It erases information, but however it turns out that the natural identification of supercurves in (as maps from 1 | 1 to ) with curves in E restricts to a 1 to 1 correspondence on geodesics. This bijection is induced by a natural identification of initial conditions for geodesics...

Divergence operators and odd Poisson brackets

Yvette Kosmann-Schwarzbach, Juan Monterde (2002)

Annales de l’institut Fourier

We define the divergence operators on a graded algebra, and we show that, given an odd Poisson bracket on the algebra, the operator that maps an element to the divergence of the hamiltonian derivation that it defines is a generator of the bracket. This is the “odd laplacian”, Δ , of Batalin-Vilkovisky quantization. We then study the generators of odd Poisson brackets on supermanifolds, where divergences of graded vector fields can be defined either in terms of berezinian volumes or of graded connections. Examples...

General construction of Banach-Grassmann algebras

Vladimir G. Pestov (1992)

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

We show that a free graded commutative Banach algebra over a (purely odd) Banach space E is a Banach-Grassmann algebra in the sense of Jadczyk and Pilch if and only if E is infinite-dimensional. Thus, a large amount of new examples of separable Banach-Grassmann algebras arise in addition to the only one example previously known due to A. Rogers.

Gerstenhaber and Batalin-Vilkovisky algebras; algebraic, geometric, and physical aspects

Claude Roger (2009)

Archivum Mathematicum

We shall give a survey of classical examples, together with algebraic methods to deal with those structures: graded algebra, cohomologies, cohomology operations. The corresponding geometric structures will be described(e.g., Lie algebroids), with particular emphasis on supergeometry, odd supersymplectic structures and their classification. Finally, we shall explain how BV-structures appear in Quantum Field Theory, as a version of functional integral quantization.

Introduction to Graded Geometry, Batalin-Vilkovisky Formalism and their Applications

Jian Qiu, Maxim Zabzine (2011)

Archivum Mathematicum

These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The BV–formalism is introduced through an odd Fourier transform and the algebraic aspects of integration theory are stressed. As a main application we consider the perturbation theory for certain finite dimensional integrals within BV-formalism. As an illustration we present...

Modular classes of Q-manifolds: a review and some applications

Andrew James Bruce (2017)

Archivum Mathematicum

A Q-manifold is a supermanifold equipped with an odd vector field that squares to zero. The notion of the modular class of a Q-manifold – which is viewed as the obstruction to the existence of a Q-invariant Berezin volume – is not well know. We review the basic ideas and then apply this technology to various examples, including L -algebroids and higher Poisson manifolds.

Non-split almost complex and non-split Riemannian supermanifolds

Matthias Kalus (2019)

Archivum Mathematicum

Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. For almost complex structures, the existence of a splitting is equivalent to the existence of local coordinates in which the almost complex structure can be represented by a purely numerical matrix, i.e. containing no Grassmann variables. For Riemannian metrics, terms up to degree 2 are allowed in...

On curves and jets of curves on supermanifolds

Andrew James Bruce (2014)

Archivum Mathematicum

In this paper we examine a natural concept of a curve on a supermanifold and the subsequent notion of the jet of a curve. We then tackle the question of geometrically defining the higher order tangent bundles of a supermanifold. Finally we make a quick comparison with the notion of a curve presented here are other common notions found in the literature.

Currently displaying 1 – 20 of 35

Page 1 Next