Related papers: Samelson products in p-regular exceptional Lie gro…
We define the thin fundamental categorical group ${\mathcal P}_2(M,*)$ of a based smooth manifold $(M,*)$ as the categorical group whose objects are rank-1 homotopy classes of based loops on $M$, and whose morphisms are rank-2 homotopy…
We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also…
An associative ring with 1 is said to be semilocal provided it is semisimple artinian modulo its Jacobson radical, that is, modulo its Jacobson radical it is isomorphic to a finite product of matrices over division rings. Modules with a…
We prove that if a finite group $G$ has a representation with fixity $f$, then it acts freely and homologically trivially on a finite CW-complex homotopy equivalent to a product of $f+1$ spheres. This shows, in particular, that every finite…
We describe simply connected compact exceptional simple Lie groups in very elementary way. We first construct all simply connected compact exceptional Lie groups G concretely. Next, we find all involutive automorphisms of G, and determine…
The Lie-Poisson analogues of the cotangent bundle and coadjoint orbits of a Lie group are considered. For the natural Poisson brackets the symplectic leaves in these manifolds are classified and the corresponding symplectic forms are…
By considering suitable Poisson groupoids, we develop an approach to obtain Lie group structures on (subgroups of) the Poisson diffeomorphism groups of various classes of Poisson manifolds. As applications, we show that the Poisson…
Studies the cohomology of p-central, powerful, p-groups with a certain extension property. These groups are naturally associated to Lie algebras. The paper develops a machinery that calculates the first few terms of the Bockstein spectral…
A p-local compact group is an algebraic object modelled on the p-local homotopy theory of classifying spaces of compact Lie groups and p-compact groups. In the study of these objects unstable Adams operations, are of fundamental importance.…
Category theory provides a means through which many far-ranging fields of mathematics can be related by their similar structure. In a paper by Robinson [2], this interconnectivity afforded by categorical perspectives allowed for the…
We study locally compact group topologies on semisimple Lie groups. We show that the Lie group topology on such a group $S$ is very rigid: every 'abstract' isomorphism between $S$ and a locally compact and $\sigma$-compact group $\Gamma$ is…
The main result of this paper is a convexity theorem for momentum mappings of certain hamiltonian actions of noncompact semisimple Lie groups. The image is required to fall within a certain open subset D of the (dual of the) Lie algebra,…
We consider symplectic singularities in the sense of A. Beauville as examples of Poisson schemes. Using Poisson methods, we prove that a symplectic singularity admits a finite stratification with smooth symplectic strata. We also prove that…
We give simple explicit formulas for deformation quantization of Poisson-Lie groups and of similar Poisson manifolds which can be represented as moduli spaces of flat connections on surfaces. The star products depend on a choice of…
A closed subgroup of a semisimple algebraic group is called irreducible if it lies in no proper parabolic subgroup. In this paper we classify all irreducible $A_1$ subgroups of exceptional algebraic groups $G$. Consequences are given…
In this note a functorial approach to the integration problem of an LA-groupoid to a double Lie groupoid is discussed. To do that, we study the notions of fibred products in the categories of Lie groupoids and Lie algebroids, giving…
The notion of a dual polyhedral product is introduced as a generalization of Hovey's definition of Lusternik-Schnirelmann cocategory. Properties established from homotopy decompositions that relate the based loops on a polyhedral product to…
We produce an example of an irreducible discrete subgroup in the product $SL(2,\R)\times SL(2,\R)$ which is not a lattice. This answers a question asked in [15].
We introduce the notion of strong $p$-semi-regularity and show that if $p$ is a regular type which is not locally modular then any $p$-semi-regular type is strongly $p$-semi-regular. Moreover, for any such $p$-semi-regular type, "domination…
We study Patterson-Sullivan measures for a class of discrete subgroups of higher rank semisimple Lie groups, called transverse groups, whose limit set is well-defined and transverse in a partial flag variety. This class of groups includes…