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Infinitesimal unipotent group schemes of complexity 1

Rolf Farnsteiner, Gerhard Röhrle, Detlef Voigt (2001)

Colloquium Mathematicae

We classify the uniserial infinitesimal unipotent commutative groups of finite representation type over algebraically closed fields. As an application we provide detailed information on the structure of those infinitesimal groups whose distribution algebras have a representation-finite principal block.

Injective and projective properties of R [ x ] -modules

Sangwon Park, Eunha Cho (2004)

Czechoslovak Mathematical Journal

We study whether the projective and injective properties of left R -modules can be implied to the special kind of left R [ x ] -modules, especially to the case of inverse polynomial modules and Laurent polynomial modules.

Injective models of G -disconnected simplicial sets

Marek Golasiński (1997)

Annales de l'institut Fourier

We generalize the results by G.V. Triantafillou and B. Fine on G -disconnected simplicial sets. An existence of an injective minimal model for a complete 𝕀 -algebra is presented, for any E I -category 𝕀 . We then make use of the E I -category 𝒪 ( G , X ) associated with a G -simplicial set X to apply these results to the category of G -simplicial sets.Finally, we describe the rational homotopy type of a nilpotent G -simplicial set by means of its injective minimal model.

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...

Invariant differential operators on the tangent space of some symmetric spaces

Thierry Levasseur, J. Toby Stafford (1999)

Annales de l'institut Fourier

Let 𝔤 be a complex, semisimple Lie algebra, with an involutive automorphism ϑ and set 𝔨 = Ker ( ϑ - I ) , 𝔭 = Ker ( ϑ + I ) . We consider the differential operators, 𝒟 ( 𝔭 ) K , on 𝔭 that are invariant under the action of the adjoint group K of 𝔨 . Write τ : 𝔨 Der 𝒪 ( 𝔭 ) for the differential of this action. Then we prove, for the class of symmetric pairs ( 𝔤 , 𝔨 ) considered by Sekiguchi, that d 𝒟 ( 𝔭 ) : d 𝒪 ( 𝔭 ) K = 0 = 𝒟 ( 𝔭 ) τ ( 𝔨 ) . An immediate consequence of this equality is the following result of Sekiguchi: Let ( 𝔤 0 , 𝔨 0 ) be a real form of one of these symmetric pairs ( 𝔤 , 𝔨 ) , and suppose that T is a K 0 -invariant...

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