Infinite Grassmannians and moduli spaces of G-bundles.
Infinite independent systems of identities of alternative commutative algebra over a field of characteristic three
Let 𝔄₃ denote the variety of alternative commutative (Jordan) algebras defined by the identity x³ = 0, and let 𝔖₂ be the subvariety of the variety 𝔄₃ of solvable algebras of solviability index 2. We present an infinite independent system of identities in the variety 𝔄₃ ∩ 𝔖₂𝔖₂. Therefore we infer that 𝔄₃ ∩ 𝔖₂𝔖₂ contains a continuum of infinite based subvarieties and that there exist algebras with an unsolvable words problem in 𝔄₃ ∩ 𝔖₂𝔖₂. It is worth mentioning that these results were...
Infinite Root Systems, Representations of Graphs and Invariant Theory.
Infinite-dimensional hyperkähler manifolds associated with Hermitian-symmetric affine coadjoint orbits
In this paper, we construct a hyperkähler structure on the complexification of any Hermitian symmetric affine coadjoint orbit of a semi-simple -group of compact type, which is compatible with the complex symplectic form of Kirillov-Kostant-Souriau and restricts to the Kähler structure of . By a relevant identification of the complex orbit with the cotangent space of induced by Mostow’s decomposition theorem, this leads to the existence of a hyperkähler structure on compatible with...
Infinite-dimensional Lie groups and algebras in mathematical physics.
Infinitely many two-variable generalisations of the Alexander-Conway polynomial.
Infinitesimal unipotent group schemes of complexity 1
We classify the uniserial infinitesimal unipotent commutative groups of finite representation type over algebraically closed fields. As an application we provide detailed information on the structure of those infinitesimal groups whose distribution algebras have a representation-finite principal block.
Injective Modules for Restricted Enveloping Algebras.
Innere Lie-Tripelsysteme und J-Ternäre Algebren.
Integrability obstructions for extensions of Lie algebroids
Integrable connections related to zonal spherical functions.
Integrable representations of affine Lie-algebras.
Integral Quadratic Forms, Kac-Moody Algebras, and Fractional Quantum Hall Effect. An ADE- Classification
Integral structures on H-type Lie algebras.
Intégrales orbitales sur les algèbres de Lie réductives.
Intertwining symmetry algebras of quantum superintegrable systems.
Introduction to Graded Geometry, Batalin-Vilkovisky Formalism and their Applications
These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The BV–formalism is introduced through an odd Fourier transform and the algebraic aspects of integration theory are stressed. As a main application we consider the perturbation theory for certain finite dimensional integrals within BV-formalism. As an illustration we present...
Introduction to quantum Lie algebras
Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in h. They are derived from the quantized enveloping algebras . The quantum Lie bracket satisfies a generalization of antisymmetry. Representations of quantum Lie algebras are defined in terms of a generalized commutator. The recent general results about quantum Lie algebras are introduced with the help of the explicit example of .
Invariant analysis and contractions of symmetric spaces. Part I
Invariant cohomology of the Poisson Lie algebra of a symplectic manifold