We define the notion of fundamental Lie algebra of a graph of Lie algebras and show that this construction yields Mayer-Vietoris sequences. We extend some well known results in group theory to $\\mathbb{N}$-graded Lie algebras: for example, we show that one relator $\\mathbb{N}$-graded...
The Grothendieck group of the tower of symmetric group algebras has a self-dual graded Hopf algebra structure. Inspired by this, we introduce by way of axi... N Bergeron,H Li - Academic Press 被引量: 0发表: 2009年 Integer torsion in local cohomology, and questions on tight closure theory...
Using Proposition1.1and Proposition1.2we obtain the main results of this note:Theorem 1.1.LetHbe an involutory Hopf algebra,MandNtwoH-(co)modules such thatM⊗Nis (co)semisimple as aH-(co)module.The following hold:19 Serre Theorem for involutory Hopf algebras(1)IfNis finitely generated ...
Consequences of these results on the operation of a Lie group and the existence of Serre fibrations are given. We also examine various measures of rational triviality for a fibration and compare them with and whithout the hypothesis of pure fibration. DOI: 10.5802/aif.838 被引量: 55 年份...
Let R be a commutative Noetherian ring. The notion of regular sequences with respect to a Serre class of ii-rnodules is introduced and some of their essential properties are given. Then in the local case, we explore a theory of Cohen-Macaulayness with respect to Serre classes.关键词:SERRE...
The automorphism group of any factor appearing more than once does not have finite abelianisation or can be expressed as a union of a properly increasing sequence of subgroups.Then Aut(G)Aut(G) does not have Property (FA). These imply Corollary 1.1 since finite groups and their automorphism...
InterviewwithJean-PierreSerreInterviewers:MartinRaussenandChristianSkauThisinterviewtookplaceinOsloon2June2003duringtheAbelPrizecelebrations.TopologyFirst,wecongratulateyouonwinningthefirstAbelPrize.Youstartedyourcareerwithathesisthatcentredonalgebraictopology.Thiswasthen(atleastinFrance)averynewdisciplineandnotamajorarea...
We construct a counterexample to Serre's problem for over a RIT algebra, which is a noncommutative quadratic algebra, given by quadratic relations, more general than the relations of the Weyl algebra and of a universal enveloping of finite dimensional Lie algebra....
Suppose we are given a certain class of infinite dimensional Lie algebras L defined over an algebrai... P Gille,A Pianzola - 《Mathematische Annalen》 被引量: 76发表: 2007年 Variations on a theme of groups splitting by a quadratic extension and Grothendieck—Serre conjecture for group schemes...