At the present work we consider infinitesimal deformations f : x → x + εz(x) of a space LN with non-symmetric affine connection L i jk . Based on the non-symmetry of the connection, we use four kinds of covariant derivative to express the Lie derivative and the deformations. Rigidity of geometric objects (connection, tensors, curvature) is defined by virtue of Lie derivative. AMS Subj. Class.: ...

In this paper we give a method which uses a nite number of di erentiations and linear operations to determine the Cartan structure of structurally transitive Lie pseudogroups from their in nitesimal de ning equations. These equations are the linearized form of the pseudogroup de ning system { the system of pdes whose solutions are the transformations belonging to the pseudogroup. In many applic...

A simply connected topological space X has homotopy Lie algebra ( X) Q. Following Quillen, there is a connected di erential graded free Lie algebra (dgL) called a Lie model, which determines the rational homotopy type of X , and whose homology is isomorphic to the homotopy Lie algebra. We show that such a Lie model can be replaced with one that has a special property we call separated. The homo...

A Riemannian Einstein solvmanifold is called standard, if the orthogonal complement to the nilradical of its Lie algebra is abelian. No examples of nonstandard solvmanifolds are known. We show that the standardness of an Einstein metric solvable Lie algebra is completely detected by its nilradical and prove that many classes of nilpotent Lie algebras (Einstein nilradicals, algebras with less th...

The multiplicities a λ,µ of simple modules L µ in the composition series of Kac modules V λ for the Lie superalgebra gl(m/n) were described by Serganova, leading to her solution of the character problem for gl(m/n). In Serganova's algorithm all µ with nonzero a λ,µ are determined for a given λ; this algorithm turns out to be rather complicated. In this Letter a simple rule is conjectured to fin...

Recently the correlation functions of the so–called Itzykson-Zuber/Harish-Chandra integrals were computed (by one of the authors and collaborators) for all classical groups using an integration formula that relates integrals over compact groups with respect to the Haar measure and Gaussian integrals over a maximal nilpotent Lie subalgebra of their complexification. Since the integration formula...

The main difficulty in the nonrelativistic case is that one can only use a smaller group of commuting vector fields. In particular, since one cannot use the generators of the hyperbolic rotations, due to the different wave speeds, the earlier approach of Klainerman [9] breaks down. This is because the invariant Sobolev inequality that plays a key role in [9] does not hold if one uses a smaller ...

Let g be a simple, finite-dimensional Lie superalgebra over C. These have been classified by V. Kac. Unless g is a Lie algebra or a Lie superalgebra of type osp(1, 2n), the category of finite-dimensional representations of g is not semisimple; q.v. [6]. This leads to a classification problem. For example, in [3], the representation theory of sl(m,n) is worked out by showing it is wild when m,n ...

Using an extension of techniques of Ozawa and Popa, we give an example of a non-amenable strongly solid II1 factor M containing an “exotic” maximal abelian subalgebra A: as an A,A-bimodule, L(M) is neither coarse nor discrete. Thus we show that there exist II1 factors with such property but without Cartan subalgebras. It also follows from Voiculescu’s free entropy results that M is not an inter...

Braided-Lie bialgebras have been introduced by Majid, as the Lie versions of Hopf algebras in braided categories. In this paper we extend previous work of Majid and of ours to show that there is a braided-Lie bialgebra associated to each inclusion of Kac–Moody bialgebras. Doing so, we obtain many new examples of infinite-dimensional braided-Lie bialgebras. We analyze further the case of untwist...