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Displaying 41 –
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186
We develop an algebraic version of Cartan’s method of equivalence or an analog of Tanaka prolongation for the (extrinsic) geometry of curves of flags of a vector space W with respect to the action of a subgroup G of GL(W). Under some natural assumptions on the subgroup G and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure linear algebra. The scope...
We describe a spectral sequence for computing Leibniz cohomology for Lie algebras.
The category of group-graded modules over an abelian group is a monoidal category. For any bicharacter of this category becomes a braided monoidal category. We define the notion of a Lie algebra in this category generalizing the concepts of Lie super and Lie color algebras. Our Lie algebras have -ary multiplications between various graded components. They possess universal enveloping algebras that are Hopf algebras in the given category. Their biproducts with the group ring are noncommutative...
Let be an associative and commutative ring with , a subring of such that , an integer. The paper describes subrings of the general linear Lie ring that contain the Lie ring of all traceless matrices over .
We reduce the problem on multiplicities of simple subquotients in an -stratified generalized Verma module to the analogous problem for classical Verma modules.
Let be a reductive algebraic group, a parabolic subgroup of with unipotent radical , and a closed connected subgroup of which is normalized by . We show that acts on with finitely many orbits provided is abelian. This generalizes a well-known finiteness result, namely the case when is central in . We also obtain an analogous result for the adjoint action of on invariant linear subspaces of the Lie algebra of which are abelian Lie algebras. Finally, we discuss a connection...
Results on derivations and automorphisms of some quantum and classical Poisson algebras, as well as characterizations of manifolds by the Lie structure of such algebras, are revisited and extended. We prove in particular a somewhat unexpected fact that the algebras of linear differential operators acting on smooth sections of two real vector bundles of rank 1 are isomorphic as Lie algebras if and only if the base manifolds are diffeomorphic, whether or not the line bundles themselves are isomorphic....
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