Displaying similar documents to “Coalgebraic Approach to the Loday Infinity Category, Stem Differential for 2 n -ary Graded and Homotopy Algebras”

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

Jian Qiu, Maxim Zabzine (2011)

Archivum Mathematicum

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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...

Transgression and Clifford algebras

Rudolf Philippe Rohr (2009)

Annales de l’institut Fourier

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Let W be a differential (not necessarily commutative) algebra which carries a free action of a polynomial algebra S P with homogeneous generators p 1 , ⋯ , p r . We show that for W acyclic, the cohomology of the quotient H ( W / < p 1 , ⋯ , p r > ) is isomorphic to a Clifford algebra Cl ( P , B ) , where the (possibly degenerate) bilinear form B depends on W . This observation is an analogue of an old result of Borel in a non-commutative context. As an application, we study the case of W given by the quantized Weil algebra...

Shuffle bialgebras

María Ronco (2011)

Annales de l’institut Fourier

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The goal of our work is to study the spaces of primitive elements of some combinatorial Hopf algebras, whose underlying vector spaces admit linear basis labelled by subsets of the set of maps between finite sets. In order to deal with these objects we introduce the notion of shuffle algebras, which are coloured algebras where composition is not always defined. We define bialgebras in this framework and compute the subpaces of primitive elements associated to them. These spaces of primitive...

On the classification of 3-dimensional coloured Lie algebras

Sergei Silvestrov (1997)

Banach Center Publications

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In this paper, complex 3-dimensional Γ-graded ε-skew-symmetric and complex 3-dimensional Γ-graded ε-Lie algebras with either 1-dimensional or zero homogeneous components are classified up to isomorphism.