Related papers: Loop groups and string topology
Let G be a reductive algebraic group over a field of prime characteristic. One can associate to G (or subgroups thereof) its Lie algebra, its Frobenius kernels, and the finite Chevalley group of points over a finite field. The…
We consider various generalisations of the string class of a loop group bundle. The string class is the obstruction to lifting a bundle whose structure group is the loop group $LG$ to one whose structure group is the Kac-Moody central…
The aim of the present paper is to provide a comprehensive introduction to some algebraic and geometric aspects of real representations of compact Lie groups, as well as some results concerning isotropy strata and restriction of invariants.
In these lectures I review the progress made over the last few years in the subject of string and string-inspired phenomenology. I take a practical approach, thereby concentrating more on explicit examples rather than on formal…
In these lectures we review the quantum physics of large Schwarzschild black holes. Hawking's information paradox, the theory of the stretched horizon and the principle of black hole complementarity are covered. We then discuss how the…
This is a selection of open problems dealing with ``large'' (non locally compact) topological groups and concerning extreme amenability (fixed point on compacta property), oscillation stability, universal minimal flows and other aspects of…
The representation sets of central loops are investigated and the results obtained are used to construct a finite C-loop. It is shown that for certain types of isotopisms, the central identities are isotopic invariant.
This is an expanded version of the notes of our lectures given at the conference "Current Developments in Mathematics 2003" held at Harvard University on November 21--22, 2003. We present an overview of the main definitions, results and…
We study the extension of a Lie algebroid by a representation up to homotopy, including semidirect products of a Lie algebroid with such representations. The extension results in a higher Lie algebroid. We give exact Courant algebroids and…
Three lectures on effective field theory given at the Seventh Summer School in Nuclear Physics, Seattle June 19-30 1995.
The causal representation of multi-loop scattering amplitudes, obtained from the application of the loop-tree duality formalism, comprehensively elucidates, at integrand level, the behaviour of only physical singularities. This…
In this paper, we present a study on the prolongations of representations of Lie algebras. We show that a tangent bundle of a given Lie algebra attains a Lie algebra structure. Then, we prove that this tangent bundle is algebraically…
These proceedings are based on lectures delivered at the "RTN Winter School on Strings, Supergravity and Gauge Theories", CERN, January 16 - January 20, 2006. The school was mainly aimed at Ph.D. students and young postdocs. The lectures…
In this talk I study the topology of mathematically idealised center vortices, defined in a gauge invariant way as closed (infinitely thin) flux surfaces (in D=4 dimensions) which contribute the $n^{th}$ power of a non-trivial center…
These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and…
This article surveys the application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems. The common thread in the discussion is the construction of quantum fields using…
These notes form an introduction to Lie algebras and group theory. Most of the material can be found in many works by various authors given in the list of references. The reader is referred to such works for more detail.
This is a summary of a talk given at the "Conference on Pure and Applied Topology", Isle of Skye, June 24, 2005. It contains an announcement and sketch of proof of the classification of 2-compact groups.
The goal of this paper is two-fold. First we provide the information needed to study Bol, $A_r$ or Bruck loops by applying group theoretic methods. This information is used in this paper as well as in [BS3] and in [S]. Moreover, we…
Let $G$ be a compact connected Lie group and $k \in H^4(BG,\mathbb{Z})$ a cohomology class. The String 2-group $G_k$ is the central extension of $G$ by the 2-group $[\ast/U(1)]$ classified by $k$. It has a close relationship to the level…