Page 1 Next

Displaying 1 – 20 of 30

Showing per page

A Riemann-Roch theorem for dg algebras

François Petit (2013)

Bulletin de la Société Mathématique de France

Given a smooth proper dg algebra A , a perfect dg A -module M and an endomorphism f of M , we define the Hochschild class of the pair ( M , f ) with values in the Hochschild homology of the algebra A . Our main result is a Riemann-Roch type formula involving the convolution of two such Hochschild classes.

Artin-Schelter regular algebras of dimension five

Gunnar Fløystad, Jon Eivind Vatne (2011)

Banach Center Publications

We show that there are exactly three types of Hilbert series of Artin-Schelter regular algebras of dimension five with two generators. One of these cases (the most extreme) may not be realized by an enveloping algebra of a graded Lie algebra. This is a new phenomenon compared to lower dimensions, where all resolution types may be realized by such enveloping algebras.

Description de certains super groupes classiques

Caroline Gruson (1994)

Annales de l'institut Fourier

La première partie de cet article est une adaptation au cadre des super groupes d’un théorème dû à Cartier qui assure que les groupes formels sont lisses en caractéristique zéro. La seconde partie donne une description des super groupes de Lie dits “vraiment classiques” comme groupes d’automorphismes de super algèbres semi-simples associatives à involution, selon une méthode de Weil.

Explicit cogenerators for the homotopy category of projective modules over a ring

Amnon Neeman (2011)

Annales scientifiques de l'École Normale Supérieure

Let R be a ring. In two previous articles [12, 14] we studied the homotopy category 𝐊 ( R - Proj ) of projective R -modules. We produced a set of generators for this category, proved that the category is 1 -compactly generated for any ring R , and showed that it need not always be compactly generated, but is for sufficiently nice R . We furthermore analyzed the inclusion j ! : 𝐊 ( R - Proj ) 𝐊 ( R - Flat ) and the orthogonal subcategory 𝒮 = 𝐊 ( R - Proj ) . And we even showed that the inclusion 𝒮 𝐊 ( R - Flat ) has a right adjoint; this forces some natural map to be an equivalence...

Geometry of noncommutative algebras

Eivind Eriksen, Arvid Siqveland (2011)

Banach Center Publications

There has been several attempts to generalize commutative algebraic geometry to the noncommutative situation. Localizations with good properties rarely exist for noncommutative algebras, and this makes a direct generalization difficult. Our point of view, following Laudal, is that the points of the noncommutative geometry should be represented as simple modules, and that noncommutative deformations should be used to obtain a suitable localization in the noncommutative situation. Let A be an algebra...

Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products

Pavel Etingof, Wee Liang Gan, Victor Ginzburg, Alexei Oblomkov (2007)

Publications Mathématiques de l'IHÉS

The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflection functors and shift functors for generalized preprojective algebras and symplectic reflection algebras...

Localizations for construction of quantum coset spaces

Zoran Škoda (2003)

Banach Center Publications

Viewing comodule algebras as the noncommutative analogues of affine varieties with affine group actions, we propose rudiments of a localization approach to nonaffine Hopf algebraic quotients of noncommutative affine varieties corresponding to comodule algebras. After reviewing basic background on noncommutative localizations, we introduce localizations compatible with coactions. Coinvariants of these localized coactions give local information about quotients. We define Zariski locally trivial quantum...

Noncommutative algebraic geometry.

Olav A. Laudal (2003)

Revista Matemática Iberoamericana

The need for a noncommutative algebraic geometry is apparent in classical invariant and moduli theory. It is, in general, impossible to find commuting parameters parametrizing all orbits of a Lie group acting on a scheme. When one orbit is contained in the closure of another, the orbit space cannot, in a natural way, be given a scheme structure. In this paper we shall show that one may overcome these difficulties by introducing a noncommutative algebraic geometry, where affine schemes are modeled...

Currently displaying 1 – 20 of 30

Page 1 Next