Search results for "Jordan"

Varieties of almost polynomial growth: classifying their subvarieties

2007

Let G be the infinite dimensional Grassmann algebra over a field F of characteristic zero and UT2 the algebra of 2 x 2 upper triangular matrices over F. The relevance of these algebras in PI-theory relies on the fact that they generate the only two varieties of almost polynomial growth, i.e., they grow exponentially but any proper subvariety grows polynomially. In this paper we completely classify, up to PI-equivalence, the associative algebras A such that A is an element of Var(G) or A is an element of Var(UT2).

Matrix algebras of polynomial codimension growth

2007

We study associative algebras with unity of polynomial codimension growth. For any fixed degree $k$ we construct associative algebras whose codimension sequence has the largest and the smallest possible polynomial growth of degree $k$. We also explicitly describe the identities and the exponential generating functions of these algebras.

Polynomial identities for the Jordan algebra of a degenerate symmetric bilinear form

2013

Let J(n) be the Jordan algebra of a degenerate symmetric bilinear form. In the first section we classify all possible G-gradings on J(n) where G is any group, while in the second part we restrict our attention to a degenerate symmetric bilinear form of rank n - 1, where n is the dimension of the vector space V defining J(n). We prove that in this case the algebra J(n) is PI-equivalent to the Jordan algebra of a nondegenerate bilinear form.

Almost polynomial growth: Classifying varieties of graded algebras

2015

Let G be a finite group, V a variety of associative G-graded algebras and c (V), n = 1, 2, …, its sequence of graded codimensions. It was recently shown by Valenti that such a sequence is polynomially bounded if and only if V does not contain a finite list of G-graded algebras. The list consists of group algebras of groups of order a prime number, the infinite-dimensional Grassmann algebra and the algebra of 2 × 2 upper triangular matrices with suitable gradings. Such algebras generate the only varieties of G-graded algebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety is polynomially bounded. In this paper we completely classify all sub…

Un nouvel invariant des algèbres de Lie et des super-algèbres de Lie quadratiques

2011

In this thesis, we defind a new invariant of quadratic Lie algebras and quadratic Lie superalgebras and give a complete study and classification of singular quadratic Lie algebras and singular quadratic Lie superalgebras, i.e. those for which the invariant does not vanish. The classification is related to adjoint orbits of Lie algebras o(m) and sp(2n). Also, we give an isomorphic characterization of 2-step nilpotent quadratic Lie algebras and quasi-singular quadratic Lie superalgebras for the purpose of completeness. We study pseudo-Euclidean Jordan algebras obtained as double extensions of a quadratic vector space by a one-dimensional algebra and 2-step nilpotent pseudo-Euclidean Jordan al…

Two new species of Lygaeidae from the Middle East

2007

Iris bismarckiana in Israel and Jordan—New findings and taxonomic remarks

2001

Iris bismarckiana (Iris section Oncocyclus) was found for the first time in the west Gilead in Jordan. This discovery was utilized to shed some light on the taxonomic relationships among the light-colored irises in the Levant. Morphometric quantitative analysis of the Jordanian population compared to I. bismarckiana allies in Israel (I. bismarckiana in the Galilee and I. hermona in the Golan) suggests that the Jordanian population is I. bismarckiana, despite the large distance from the main distribution area. Cluster analysis, based on the morphology, revealed that some of the populations of I. bismarckiana have closer affinities to I. hermona than to each other. Populations of I. hermona a…

MR3106093 Reviewed Łochowski, Rafał M. On a generalisation of the Hahn-Jordan decomposition for real càdlàg functions. Colloq. Math. 132 (2013), no. …

2013

Mapping the geometry of the F(4) group.

2007

In this paper we present a construction of the compact form of the exceptional Lie group F4 by exponentiating the corresponding Lie algebra f4. We realize F4 as the automorphisms group of the exceptional Jordan algebra, whose elements are 3 x 3 hermitian matrices with octonionic entries. We use a parametrization which generalizes the Euler angles for SU(2) and is based on the fibration of F4 via a Spin(9) subgroup as a fiber. This technique allows us to determine an explicit expression for the Haar invariant measure on the F4 group manifold. Apart from shedding light on the structure of F4 and its coset manifold OP2=F4/Spin(9), the octonionic projective plane, these results are a prerequisi…

On growth of codimensions of Jordan algebras

2011