Related papers: An Integrability Condition for Simple Lie Groups I…

Winkelmann considered compact complex manifolds $X$ equipped with a reduced effective normal crossing divisor $D\, \subset\, X$ such that the logarithmic tangent bundle $TX(-\log D)$ is holomorphically trivial. He characterized them as…

Let $G$ be a finite group, $p$ a prime, and $(K,\mathcal{O},F)$ a $p$-modular system. We prove that the trivial source ring of $\mathcal{O} G$ is isomorphic to the ring of {\em coherent} $G$-stable tuples $(\chi_P)$, where $\chi_P$ is a…

Given a group G, a (unital) ring A and a group homomorphism $\sigma : G \to \Aut(A)$, one can construct the skew group ring $A \rtimes_{\sigma} G$. We show that a skew group ring $A \rtimes_{\sigma} G$, of an abelian group G, is simple if…

We prove that if $G$ is a finite simple group of Lie type and $S_1,\dots, S_k$ are subsets of $G$ satisfying $\prod_{i=1}^k|S_i|\geq|G|^c$ for some $c$ depending only on the rank of $G$, then there exist elements $g_1,\dots, g_k$ such that…

We prove that a generic Steiner bundle E is simple if and only if the Euler characteristic of the endomorphism bundle of E is less or equal to 1. In particular we show that either E is exceptional or it satisfies the following inequality…

This is a continuation of our paper math.AG/0111298. We prove an explicit formula for the geometric genus p_g of a quasihomogeneous isolated surface singularity in terms of the Seiberg-Witten invariant of the link and other topological data…

If a compact quantum group acts faithfully and smoothly (in the sense of Goswami 2009) on a smooth, compact, oriented, connected Riemannian manifold such that the action induces a natural bimodule morphism on the module of sections of the…

It is shown that if A is a separable, exact C*-algebra which satisfies the Universal Coefficient Theorem (UCT) and has a faithful, amenable trace, then A admits a trace-preserving embedding into a simple, unital AF-algebra with unique…

Let X be a compact Kaehler manifold of complex dimension n. Let G be a connected solvable subgroup of the automorphism group Aut(X), and let N(G) be the normal subgroup of G of elements of null entropy. One of the goals of this paper is to…

In this paper we answer two long-standing questions in the classification of $G$-torsors on curves for an almost simple, simply connected algebraic group $G$ over the field of complex numbers. The first question is to give an intrinsic…

Let $\mathfrak{g}$ be a Lie algebra over an algebraically closed field $\Bbbk$ of characteristic zero. Define the universal grading group $\mathcal{C}(\mathfrak{g})$ as having one generator $g_{\rho}$ for each irreducible…

Let G be a complex semi-simple linear algebraic group without G_2 factors, B a Borel subgroup of G and T a maximal torus in B. The flag variety G/B is a projective G-homogeneous variety whose tangent space at the identity coset is…

A ring A is called presimplifiable if whenever a; b belongs to A and a = ab, then either a = 0 or b is a unit in A. Let A be a commutative ring and G be an abelian torsion group. For the group ring A[G], we prove that A[G] is…

Let $G_1$ and $G_2$ be Lie groups furnished with bi-invariant metrics and $f:G_1\rightarrow G_2$ be a Lie group homomorphism which is also a minimal isometric immersion. If $G_1$ is compact and connected, we prove that either $G_1$ is…

We consider actions of non-compact simple Lie groups preserving an analytic rigid geometric structure of algebraic type on a compact manifold. The structure is not assumed to be unimodular, so an invariant measure may not exist. Ergodic…

The notion of rigidity of Lie algebra is linked to the following problem: when does a Lie brackets $\mu$ on a vector space g satisfy that every Lie bracket $\mu_1$ sufficiently close to $\mu$ is of the form $\mu_1 = P.\mu $ for some P in…

We prove that among all compact homogeneous spaces for an effective transitive action of a Lie group whose Levi subgroup has no compact simple factors, the seven-dimensional flat torus is the only one that admits an invariant torsion-free…

We prove that the twisted K-homology of a simply connected simple Lie group G of rank n is an exterior algebra on n-1 generators tensor a cyclic group. We give a detailed description of the order of this cyclic group in terms of the…

We consider left-invariant $G_2$-structures on $7$-dimensional almost Abelian Lie groups. Also, we characterise the associated torsion forms and the full torsion tensor according to the Lie bracket $A$ of the corresponding Lie algebra. In…

Let P be a parabolic subgroup of a semisimple complex Lie group G defined by a subset \Sigma of simple roots of G, and let E_\phi be a homogeneous vector bundle over the flag manifold G/P corresponding to a linear representation \phi of P.…