-homologie et -homologie dans la catégorie des -modules différentiables
Gateaux Differentials in Banach Algebras.
Gelfand-Kirillor Dimension for non-Associative Algebras
Gel'fand-Kirillov dimension for algebras associated with the Weyl algebra
Gelfand-Kirillov Dimension for Harish-Chandra Modules.
General construction of Banach-Grassmann algebras
We show that a free graded commutative Banach algebra over a (purely odd) Banach space is a Banach-Grassmann algebra in the sense of Jadczyk and Pilch if and only if is infinite-dimensional. Thus, a large amount of new examples of separable Banach-Grassmann algebras arise in addition to the only one example previously known due to A. Rogers.
General structured bundles
Summary: [For the entire collection see Zbl 0742.00067.]A general theory of fibre bundles structured by an arbitrary differential-geometric category is presented. It is proved that the structured bundles of finite type coincide with the classical associated bundles.
Generalised Jantzen filtration of Lie superalgebras I
A Jantzen type filtration for generalised Verma modules of Lie superalgebras is introduced. In the case of type I Lie superalgebras, it is shown that the generalised Jantzen filtration for any Kac module is the unique Loewy filtration, and the decomposition numbers of the layers of the filtration are determined by the coefficients of inverse Kazhdan–Lusztig polynomials. Furthermore, the length of the Jantzen filtration for any Kac module is determined explicitly in terms of the degree of atypicality...
Generalization of the formula of Faa di Bruno for a composite function with a vector argument.
Generalized atypical supertableaux for superunitary and orthosymplectic groups
Generalized derivations of Lie triple systems
In this paper, we present some basic properties concerning the derivation algebra Der (T), the quasiderivation algebra QDer (T) and the generalized derivation algebra GDer (T) of a Lie triple system T, with the relationship Der (T) ⊆ QDer (T) ⊆ GDer (T) ⊆ End (T). Furthermore, we completely determine those Lie triple systems T with condition QDer (T) = End (T). We also show that the quasiderivations of T can be embedded as derivations in a larger Lie triple system.
Generalized Gaudin models and Riccatians
The systems of differential equations whose solutions exactly coincide with Bethe ansatz solutions for generalized Gaudin models are constructed. These equations are called the generalized spectral Riccati equations, because the simplest equation of this class has a standard Riccatian form. The general form of these equations is , i=1,..., r, where denote some homogeneous polynomials of degrees constructed from functional variables and their derivatives. It is assumed that . The problem...
Generalized Hurwitz maps of the type S × V → W, anti-involutions, and quantum braided Clifford algebras
The notion of a -triple is studied in connection with a geometrical approach to the generalized Hurwitz problem for quadratic or bilinear forms. Some properties are obtained, generalizing those derived earlier by the present authors for the Hurwitz maps S × V → V. In particular, the dependence of each scalar product involved on the symmetry or antisymmetry is discussed as well as the configurations depending on various choices of the metric tensors of scalar products of the basis elements. Then...
Generalized Kac-Moody algebras and the modular function j.
Generalized Lie bialgebroids and strong Jacobi-Nijenhuis structures.
Generalized projective geometries: General theory and equivalance with Jordan structures.
Generalized radical rings, unknotted biquandles, and quantum groups
Generalized radical rings (braces) were introduced for the study of set-theoretical solutions of the quantum Yang-Baxter equation. We discuss their relationship to groups of I-type, virtual knot theory, and quantum groups.
Generalized Verma module homomorphisms in singular character
In this paper we study invariant differential operators on manifolds with a given parabolic structure. The model for the parabolic geometry is the quotient of the orthogonal group by a maximal parabolic subgroup corresponding to crossing of the -th simple root of the Dynkin diagram. In particular, invariant differential operators discussed in the paper correspond (in a flat model) to the Dirac operator in several variables.
Generalized Verma modules, loop space cohomology and MacDonald-type identities
Generalized weights for operator Lie algebras