1,720,976 research outputs found
SPIN(9) GEOMETRY OF THE OCTONIONIC HOPF FIBRATION
Full text linkWe deal with Riemannian properties of the octonionic Hopf fibration S-15 -> S-8, in terms of the structure given by its symmetry group Spin(9). In particular, we show that any vertical vector field has at least one zero, thus reproving the non-existence of S-1 subfibrations. We then discuss Spin(9)-structures from a conformal viewpoint and determine the structure of compact locally conformally parallel Spin(9)-manifolds. Eventually, we give a list of examples of locally conformally parallel Spin(9)-manifolds
Blocks and Projective Modules for Reduced Universal Enveloping Algebras of a Nilpotent Restricted Lie Algebra
No full textExistence of Solutions of the Classical Yang-Baxter Equation for a Real Lie Algebra
Full text linkWe characterize finite-dimensional Lie algebras over the real numbers for which the classical Yang-Baxter equation has a non-trivial skew-symmetric solution (resp. a non-trivial solution with invariant symmetric part). Equivalently, we obtain a characterization of those finite-dimensional real Lie algebras which admit a non-trivial (quasi-) triangular Lie bialgebra structure
On the Cohomology of Modular Lie Algebras
No full textIn this paper we establish a connection between the cohomology of a finite-dimensional modular Lie algebra and its finite-dimensional p-envelopes. We also compute the cohomology of Zassenhaus algebra and their minimal p-envelopes with coefficients in generalized baby Verma modules and in simple modules over fields of characteristic p \u3e 2
Injective Modules and Prime Ideals of Universal Enveloping Algebras
Full text linkIn this paper we study injective modules over universal enveloping algebras of finite-dimensional Lie algebras over fields of arbitrary characteristic. Most of our results are dealing with fields of prime characteristic but we also elaborate on some of their analogues for solvable Lie algebras over fields of characteristic zero. It turns out that analogous results in both cases are often quite similar and resemble those familiar from commutative ring theory
Leibniz algebras as non-associative algebras
Full text linkIn this paper we define the basic concepts for left or right Leibniz algebras and prove some of the main results. Our proofs are often variations of the known proofs but several results seem to be new
Restricted Lie Algebras with Bounded Cohomology and Related Classes of Algebras
No full textWe determine the structure of restricted Lie algebras with bounded cohomology over arbitrary fields of prime characteristic. As a byproduct a classification of the serial restricted Lie algebras and the restricted Lie algebras of finite representation type is obtained. In addition, we derive complete information on the finite dimensional indecomposable restricted modules of these algebras over algebraically closed fields
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