Related papers: Kac-Moody algebras and the cde-triangle
To every elliptic Calabi-Yau threefold with a section $X$ there can be associated a Lie group $G$ and a representation $\rho$ of that group. The group is determined from the Weierstrass model, which has singularities that are generically…
We show that certain C*-algebras which have been studied among others by Arzumanian, Vershik, Deaconu, and Renault in connection to a measure preserving transformation of a measure space and/or to a covering map of a compact space are…
We introduce a global Cauchy-Riemann($CR$)-invariant and discuss its behavior on the moduli space of $CR$-structures. We argue that this study is related to the Smale conjecture in 3-topology and the problem of counting complex structures.…
For any topological space there is a sheaf cohomology. A Grothendieck topology is a generalization of the classical topology such that it also possesses a sheaf cohomology. On the other hand any noncommutative $C^*$-algebra is a…
In a previous paper, we introduced Mysterious Triality as an extension, via algebraic topology in the form of rational homotopy theory, of Mysterious Duality by Iqbal, Neitzke, and Vafa, which provides connections between physics, in the…
The formulation of gravity and M-theories as very-extended Kac-Moody invariant theories is reviewed. Exact solutions describing intersecting extremal brane configurations smeared in all directions but one are presented. The intersection…
The aim of this paper is to explain how to get a complex of smooth representations out of the dual vector space to a smooth representation of a p-adic Lie group, in natural characteristic. The construction does not depend on any…
This report contains the results of the Workshop on the CKM Unitarity Triangle, held at CERN on 13-16 February 2002 to study the determination of the CKM matrix from the available data of K, D, and B physics. This is a coherent document…
We prove that the forgetful functors from the categories of $C^*$- and $W^*$-algebras to Banach $*$-algebras, Banach algebras or Banach spaces are all monadic, answering a question of J.Rosick\'{y}, and that the categories of unital…
These are the notes for a Part III course given in the University of Cambridge in autumn 1998. They contain an exposition of the representation theory of the Lie algebras of compact matrix groups, affine Kac-Moody algebras and the Virasoro…
Borcherds algebras represent a new class of Lie algebras which have almost all the properties that ordinary Kac-Moody algebras have, and the only major difference is that these generalized Kac-Moody algebras are allowed to have imaginary…
We investigate some of the motivations and consequences of the conjecture that the Kac-Moody algebra E11 is the symmetry algebra of M-theory, and we develop methods to aid the further investigation of this idea. The definitions required to…
These notes provide a concise introduction to the representation theory of reductive algebraic groups in positive characteristic, with an emphasis on Lusztig's character formula and geometric representation theory. They are based on the…
It has previously been proposed that the the theory of strings and branes possesses a large symmetry group generated by the Kac-Moody algebra $E_{11}$. It has also previously been proposed that the the theory of gravitation in four…
These are notes from a 3-lecture course given by V. Dokchitser at the ICTP in Trieste, Italy, 1st--5th of September 2014, as part of a graduate summer school on "L-functions and modular forms". The course is meant to serve as an…
Given a two-dimensional substitution tiling space, we show that, under some reasonable assumptions, the $K$-theory of the groupoid $C^\ast$-algebra of its unstable groupoid can be explicitly reconstructed from the $K$-theory of the…
This work provides a generalization of the Gelfand duality to the context of noncommutative locally $C^*$ algebras. Using a reformulation of a theorem proven by Dauns and Hofmann in the 60's we show that every locally $C^*$ algebra can be…
In the theory of C*-algebras, interesting noncommutative structures arise as deformations of the tensor product. For instance, the rotation algebra may be seen as a scalar twist deformation of the tensor product of the functions on the…
Exact duality in supersymmetric gauge theories leads to highly non-trivial predictions about the moduli spaces of BPS monopole solutions. These notes attempt to be a pedagogical review of the current status of these investigations and are…
The role of Kac-Moody algebras in exploiting symmetries of particle physics and string theory is described.