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
Invariant cones in Lie algebras.
Invariant cones in solvable Lie algebras.
Invariant convex sets and functions in Lie algebras.
Invariant differential operators on the tangent space of some symmetric spaces
Let be a complex, semisimple Lie algebra, with an involutive automorphism and set , . We consider the differential operators, , on that are invariant under the action of the adjoint group of . Write for the differential of this action. Then we prove, for the class of symmetric pairs considered by Sekiguchi, that . An immediate consequence of this equality is the following result of Sekiguchi: Let be a real form of one of these symmetric pairs , and suppose that is a -invariant...
Invariant measures and controllability of finite systems on compact manifolds
A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.
Invariant measures and controllability of finite systems on compact manifolds
A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.
Invariant measures and controllability of finite systems on compact manifolds
A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.
Invariant nonassociative algebra structures on irreducible representations of simple Lie algebras.
Invariant operators of inhomogeneous unitary group
Invariant orders in simply connected Lie groups.
Invariant theory and the algebra with negative integral central charge
The vertex algebra with central charge may be defined as a module over the universal central extension of the Lie algebra of differential operators on the circle. For an integer , it was conjectured in the physics literature that should have a minimal strong generating set consisting of elements. Using a free field realization of due to Kac–Radul, together with a deformed version of Weyl’s first and second fundamental theorems of invariant theory for the standard representation of ,...