Search results for "Identitie"

On algebras of polynomial codimension growth

2016

Let A be an associative algebra over a field F of characteristic zero and let $$c_n(A), n=1, 2, \ldots $$ , be the sequence of codimensions of A. It is well-known that $$c_n(A), n=1, 2, \ldots $$ , cannot have intermediate growth, i.e., either is polynomially bounded or grows exponentially. Here we present some results on algebras whose sequence of codimensions is polynomially bounded.

Group graded algebras and multiplicities bounded by a constant

2013

AbstractLet G be a finite group and A a G-graded algebra over a field of characteristic zero. When A is a PI-algebra, the graded codimensions of A are exponentially bounded and one can study the corresponding graded cocharacters via the representation theory of products of symmetric groups. Here we characterize in two different ways when the corresponding multiplicities are bounded by a constant.

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).

On almost nilpotent varieties of subexponential growth

2015

Abstract Let N 2 be the variety of left-nilpotent algebras of index two, that is the variety of algebras satisfying the identity x ( y z ) ≡ 0 . We introduce two new varieties, denoted by V sym and V alt , contained in the variety N 2 and we prove that V sym and V alt are the only two varieties almost nilpotent of subexponential growth.

Polynomial identities on superalgebras and exponential growth

2003

Abstract Let A be a finitely generated superalgebra over a field F of characteristic 0. To the graded polynomial identities of A one associates a numerical sequence {cnsup(A)}n⩾1 called the sequence of graded codimensions of A. In case A satisfies an ordinary polynomial identity, such sequence is exponentially bounded and we capture its exponential growth by proving that for any such algebra lim n→∞ c n sup (A) n exists and is a non-negative integer; we denote such integer by supexp(A) and we give an effective way for computing it. As an application, we construct eight superalgebras Ai, i=1,…,8, characterizing the identities of any finitely generated superalgebra A with supexp(A)>2 in the f…

Proper identities, Lie identities and exponential codimension growth

2008

Abstract The exponent exp ( A ) of a PI-algebra A in characteristic zero is an integer and measures the exponential rate of growth of the sequence of codimensions of A [A. Giambruno, M. Zaicev, On codimension growth of finitely generated associative algebras, Adv. Math. 140 (1998) 145–155; A. Giambruno, M. Zaicev, Exponential codimension growth of P.I. algebras: An exact estimate, Adv. Math. 142 (1999) 221–243]. In this paper we study the exponential rate of growth of the sequences of proper codimensions and Lie codimensions of an associative PI-algebra. We prove that the corresponding proper exponent exists for all PI-algebras, except for some algebras of exponent two strictly related to t…

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.

El proyecto artístico Mujeres Maestras en Perú, Colombia y Ecuador

2017

[EN] Mujeres Maestras (Women Teacher Project) is a tribute to the teachers who bring Art Education to the ArtseBased Research. We propose this inquiry from the involving teachers and students of educational centers. Through this work(in(progress(we manage the future location of exhibitions in museums and art the world. This year the exhibition visits Medellín (Colombia) and Lima (Peru). The next year planned to exhibit in Cuenca (Ecuador). Each exhibition of Mujeres Maestras consists of 21 works made exclusively for the museum or art center in which the show is organized. The graphics and the poetics of the gestures are part homage that the author gives to these women who represent a very i…

Gallivanting Round the Globe: Translating National Identities in Henry V

2012

In this article we shall be looking at the character of MacMorris in Henry V, and at his small but important role in the four captains’ scene. We shall explore some of the historical, cultural, political, dramaturgical and linguistic complexities of his portrayal of Irishness as a necessary preliminary study to its translation into other languages, both for the printed page and for the stage. Spanish and Catalan translations of the scene will be briefly analysed in what we hope will be the framework of a wider, multilingual preoccupation: how does national identity translate in a global context? How does —or can— MacMorris speak in other languages?

The development of national and European identity among children living in Italy: A cross-cultural comparison

2008