Let G be an exceptional Lie group with a maximal torus T ⊂ G. We present the integral cohomology ring H∗(G/T ) by a minimal set of Schubert classes on G/T . This completes the program of determining the integral cohomology of all complete flag manifolds G/T in the context of Schubert calculus. The results have been applied in [DZ3] to construct the integral cohomology of a simple Lie group G in...

Let $p$ be an odd prime number. In this paper, we study the growth of Sylow $p$-subgroups even $K$-groups rings integers in a $p$-adic Lie extension. Our results generalize previous Coates and Ji-Qin, where they considered situation cyclotomic $\mathbb{Z}_p$-extension. method proof differs from these work. Their relies on explicit description certain Galois group via Kummer theory afforded by c...

Using the language and terminology of relative homological algebra, in particular that of derived functors, we introduce equivariant cohomology over a general Lie-Rinehart algebra and equivariant de Rham cohomology over a locally trivial Lie groupoid in terms of suitably defined monads (also known as triples) and the associated standard constructions. This extends a characterization of equivari...

We show that the integral cohomology rings of moduli spaces stable rational marked curves are Koszul. This answers an open question Manin. Using machinery Koszul developed by Berglund, we compute homotopy Lie algebras those spaces, and obtain some estimates for Betti numbers their free loop in case torsion coefficients. also prove conjecture generalisations our main result.

We define two (n + 1) graded Lie brackets on spaces of multilinear mappings. The first one is able to recognize n-graded as-sociative algebras and their modules and gives immediately the correct differential for Hochschild cohomology. The second one recognizes n-graded Lie algebra structures and their modules and gives rise to the notion of Chevalley cohomology.

The theory of abelian categories proved very useful, providing an ax-iomatic framework for homology and cohomology of modules over a ring (in particular, abelian groups) [5]. A similar framework has been lacking for non-abelian (co)homology, the subject of which includes the categories of groups and Lie algebras etc. The point of my thesis is that semi-abelian categories (in the sense of Janeli...

We study the cohomology of the group consisting of all C∞diffeomorphisms of the line, which are C1-flat to the identity at the origin. We construct non-trivial two second real cohomology classes and uncountably many second integral homology classes of this group. 1. Notations and main results We denote by a1 the Lie algebra of all formal vector fields on R with the Krull topology. For k ≥ 0, we...

We deene two (n + 1) graded Lie brackets on spaces of multilinear mappings. The rst one is able to recognize n-graded as-sociative algebras and their modules and gives immediately the correct diierential for Hochschild cohomology. The second one recognizes n-graded Lie algebra structures and their modules and gives rise to the notion of Chevalley cohomology.