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Displaying 1161 – 1180 of 2671

On free subgroups of units in quaternion algebras

Jan Krempa (2001)

Colloquium Mathematicae

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

Jan Krempa (2003)

Colloquium Mathematicae

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

Drozd, Yu. A., Ovsienko, S. A., Futorny, V. M. (1991)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0742.00067.]Let $𝔤_{k}$ be the Lie algebra $𝔤 l (k, 𝒞)$ , and let $U_{k}$ be the universal enveloping algebra for $𝔤_{k}$ . Let $Z_{k}$ be the center of $U_{k}$ . The authors consider the chain of Lie algebras $𝔤_{n} \supset 𝔤_{n - 1} \supset \dots \supset 𝔤_{1}$ . Then $Z = 〈 Z_{k} ∣ k = 1, 2, \dots n 〉$ is an associative algebra which is called the Gel’fand-Zetlin subalgebra of $U_{n}$ . A $𝔤_{n}$ module $V$ is called a $G Z$ -module if $V = \sum_{x} \oplus V (x)$ , where the summation is over the space of characters of $Z$ and $V (x) = {v \in V ∣ {(a - x (a))}^{m} v = 0$ , $m \in 𝒵_{+}$ , $a \in 𝒵}$ . The authors describe several properties of $G Z$ - modules. For example, they prove that if $V (x) = 0$ for some $x$ ...

On generalized formal power series

Alena Vanžurová (1986)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

On generalized Jordan derivations of Lie triple systems

Abbas Najati (2010)

Czechoslovak Mathematical Journal

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 $θ$ -derivation on a Lie triple system is a $θ$ -derivation.

On generators of free color Lie superalgebras of rank two.

Aydın, Ela, Ekici, Naime (2002)

Journal of Lie Theory

On geometry of curves of flags of constant type

Boris Doubrov, Igor Zelenko (2012)

Open Mathematics

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.

Roitman, Michael (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

On Herstein's theorems relating modularity in A and A(+).

José A. Anquela (1992)

Extracta Mathematicae

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.

Sereda, V. A., Filippov, V. T. (2002)

Sibirskij Matematicheskij Zhurnal

On hyperbolic cones and mixed symmetric spaces.

Krötz, Bernhard, Neeb, Karl-Hermann (1996)

Journal of Lie Theory

On integrability of discrete representations of Lie algebra $u (p, q)$

J. Mickelsson, J. Niederle (1973)

Annales de l'I.H.P. Physique théorique

On invariants of the action of a finite group on a free Lie algebra.

Petrogradskij, V.M. (2000)

Siberian Mathematical Journal

On irreducible sl (2, R) - modules and sl 2-triples.

N. Dörr (1990)

Semigroup forum

On JB*-triples defined by fibre bundles.

Wilhelm Kaup (1995)

Manuscripta mathematica

On $k$ -filiform Lie algebras. I.

Campoamor Stursberg, O.R. (2002)

Acta Mathematica Universitatis Comenianae. New Series

On Leibniz algebras with maximal cyclic subalgebras

Vasiliy A. Chupordia, Leonid A. Kurdachenko, Igor Ya. Subbotin (2022)

Commentationes Mathematicae Universitatis Carolinae

We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras.

On Leibniz homology

Teimuraz Pirashvili (1994)

Annales de l'institut Fourier

We describe a spectral sequence for computing Leibniz cohomology for Lie algebras.

On Lie algebra decompositions, related to spherical homogeneous spaces.

Dmitri Akhiezer (1993)

Manuscripta mathematica

On Lie algebras in braided categories

Bodo Pareigis (1997)

Banach Center Publications

The category of group-graded modules over an abelian group $G$ is a monoidal category. For any bicharacter of $G$ 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 $n$ -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...

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