On formal series and infinite products over Lie algebras.
On free subgroups of units in quaternion algebras
It is well known that for the ring H(ℤ) of integral quaternions the unit group U(H(ℤ) is finite. On the other hand, for the rational quaternion algebra H(ℚ), its unit group is infinite and even contains a nontrivial free subgroup. In this note (see Theorem 1.5 and Corollary 2.6) we find all intermediate rings ℤ ⊂ A ⊆ ℚ such that the group of units U(H(A)) of quaternions over A contains a nontrivial free subgroup. In each case we indicate such a subgroup explicitly. We do our best to keep the arguments...
On free subgroups of units in quaternion algebras II
Let A ⊆ ℚ be any subring. We extend our earlier results on unit groups of the standard quaternion algebra H(A) to units of certain rings of generalized quaternions H(A,a,b) = ((-a,-b)/A), where a,b ∈ A. Next we show that there is an algebra embedding of the ring H(A,a,b) into the algebra of standard Cayley numbers over A. Using this embedding we answer a question asked in the first part of this paper.
On Gelfand-Zetlin modules
[For the entire collection see Zbl 0742.00067.]Let be the Lie algebra , and let be the universal enveloping algebra for . Let be the center of . The authors consider the chain of Lie algebras . Then is an associative algebra which is called the Gel’fand-Zetlin subalgebra of . A module is called a -module if , where the summation is over the space of characters of and , , . The authors describe several properties of - modules. For example, they prove that if for some ...
On generalized formal power series
On generalized Jordan derivations of Lie triple systems
Under some conditions we prove that every generalized Jordan triple derivation on a Lie triple system is a generalized derivation. Specially, we conclude that every Jordan triple -derivation on a Lie triple system is a -derivation.
On generators of free color Lie superalgebras of rank two.
On geometry of curves of flags of constant type
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...
On Griess algebras.
On Herstein's theorems relating modularity in A and A(+).
In this paper we will examine the relationship between modularity in the lattices of subalgebras of A and A(+), for A an associative algebra over an algebraically closed field. To this aim we will construct an ideal which measures the modularity of an algebra (not necessarily associative) in paragraph 1, examine modular associative algebras in paragraph 2, and prove in paragraph 3 that the ideal constructed in paragraph 1 coincides for A and A(+). We will also examine some properties of the ideal...
On homotopes of Novikov algebras.
On hyperbolic cones and mixed symmetric spaces.
On integrability of discrete representations of Lie algebra
On invariants of the action of a finite group on a free Lie algebra.
On irreducible sl (2, R) - modules and sl 2-triples.
On JB*-triples defined by fibre bundles.
On -filiform Lie algebras. I.
On Leibniz algebras with maximal cyclic subalgebras
We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras.
On Leibniz homology
We describe a spectral sequence for computing Leibniz cohomology for Lie algebras.
On Lie algebra decompositions, related to spherical homogeneous spaces.