We study Manin triples for a reductive Lie algebra, g. First, we generalize results of E. Karolinsky, on the classification of Lagrangian subalgebras (cf. KAROLINSKY E., A Classification of Poisson homogeneous spaces of a compact Poisson Lie group, Dokl. Ak. Nauk, 359 (1998), 13-15). Then we show that, if g is non commutative, one can attach , to each Manin triple in g , another one for a stric...

toriyeh means concealing real intention of speech using its parallel and common words so that the listener constructs from speaker's speech a meaning what he/she meant. the purpose of this research is studying jurisprudential dimensions of toriyeh in order to clarify its distinction from lying and related jurisprudential commandments by explanation of the most important discussions about t...

The crystal structures of the title compounds, 2 alpha,4 alpha-dibenzyl-3 alpha-tropanol (2 alpha,4 alpha-dibenzyl-8-methyl-8-azabicyclo[3.2.1]octan-3 alpha-ol), C(22)H(27)NO, (I), and 2 alpha,4 alpha-dibenzyl-3 beta-tropanol (2 alpha,4 alpha-dibenzyl-8-methyl-8-azabicyclo[3.2.1]octan-3 beta-ol), C(22)H(27)NO, (II), show that both compounds have a piperidine ring in a chair conformation and a p...

locally extended affine lie algebras were introduced by morita and yoshii in [j. algebra 301(1) (2006), 59-81] as a natural generalization of extended affine lie algebras. after that, various generalizations of these lie algebras have been investigated by others. it is known that a locally extended affine lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

We describe the isomorphism classes of infinite-dimensional graded Lie algebras of maximal class over fields of odd characteristic.

In order to describe non-Hamiltonian (dissipative) systems in quantum theory we need to use non-Lie algebra such that commutators of this algebra generate Lie subalgebra. It was shown that classical connection between analytic group (Lie group) and Lie algebra, proved by Lie theorems, exists between analytic loop, commutant of which is associative subloop (group), and commutant Lie algebra (an ...

Although the ideas date back to the early nineteenth century (see [1; Chapter 5] for detailed historical remarks), the theory of moving frames (“repères mobiles”) is most closely associated with the name of Élie Cartan, [12], who molded it into a powerful and algorithmic tool for studying the geometric properties of submanifolds and their invariants under the action of a transformation group. I...

where tE:R and I is the unit matrix of degree d. Let GL(K, d) denote the group of all nonsingular matrices of degree d with coefficients in K. Any subgroup of GL(K, d) will be called a linear group of degree d. Let 0 be the identity representation of a linear Lie group G with the Lie algebra 8 so that 9(x) =x (*EG). Then dd is a faithful representation of g and exp dd(X) =0(exp X) =exp X for an...

Let Θ be an arbitrary variety of algebras and let Θ0 be the category of all free finitely generated algebras from Θ. We study automorphisms of such categories for special Θ. The cases of the varieties of all groups, all semigroups, all modules over a noetherian ring, all associative and commutative algebras over a field are completely investigated. The cases of associative and Lie algebras are ...

We study the stationary and axisymmetric non-convective differentially rotating perfect-fluid solutions of Einstein’s field equations admitting one conformal symmetry. We analyse the two inequivalent Lie algebras not exhaustively considered in [1] and show that the general solution for each Lie algebra depends on one arbitrary function of one of the coordinates while a set of three ordinary dif...