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The jacobian map, the jacobian group and the group of automorphisms of the Grassmann algebra

Vladimir V. Bavula (2010)

Bulletin de la Société Mathématique de France

There are nontrivial dualities and parallels between polynomial algebras and the Grassmann algebras (e.g., the Grassmann algebras are dual of polynomial algebras as quadratic algebras). This paper is an attempt to look at the Grassmann algebras at the angle of the Jacobian conjecture for polynomial algebras (which is the question/conjecture about the Jacobian set– the set of all algebra endomorphisms of a polynomial algebra with the Jacobian $1$ – the Jacobian conjecture claims that the Jacobian...

The Mumford-Tate group of 1-motives

Cristiana Bertolin (2002)

Annales de l’institut Fourier

In this paper we study the structure and the degeneracies of the Mumford-Tate group $M T (M)$ of a 1-motive $M$ defined over $ℂ$ . This group is an algebraic $ℚ$ - group acting on the Hodge realization of $M$ and endowed with an increasing filtration $W_{•}$ . We prove that the unipotent radical of $M T (M)$ , which is $W_{- 1} (M T (M))$ , injects into a “generalized” Heisenberg group. We then explain how to reduce to the study of the Mumford-Tate group of a direct sum of 1-motives whose torus’character group and whose lattice are both of rank 1....

Displaying 21 – 26 of 26

The jacobian map, the jacobian group and the group of automorphisms of the Grassmann algebra

The Mumford-Tate group of 1-motives

Theta functions and Barsotti-Tate groups

Zerlegbare Untergruppen affiner Gruppen.

Zur Reduktion modulo p unipotenter Charaktere endlicher Chevalley-Gruppen.

Стягивание действий редуктивных алгебраических групп

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