Search results for " identities"
showing 10 items of 70 documents
Kemer, A; Averyanov, I. Some problems in PI-theory (Advances in algebra and combinatorics).
2008
This paper is devoted to a review of some of the most significant results obtained in the theory of polynomial identities and trace polynomial identities. Some of the most important problems in this area concern the relation between identities in characteristic 0 and p>0 and the classification of prime varieties. Here the authors present their achievements on the subject and makes some conjectures. Among others they give results on the classification of the multilinear identities of the prime subvarieties of the variety generated by the algebra of 2X2 matrices over a field of positive characteristic.
Matrix algebras with degenerate traces and trace identities
2022
In this paper we study matrix algebras with a degenerate trace in the framework of the theory of polynomial identities. The first part is devoted to the study of the algebra $D_n$ of $n \times n$ diagonal matrices. We prove that, in case of a degenerate trace, all its trace identities follow by the commutativity law and by pure trace identities. Moreover we relate the trace identities of $D_{n+1}$ endowed with a degenerate trace, to those of $D_n$ with the corresponding trace. This allows us to determine the generators of the trace T-ideal of $D_3$. In the second part we study commutative subalgebras of $M_k(F)$, denoted by $C_k$ of the type $F + J$ that can be endowed with the so-called st…
Trace identities and almost polynomial growth
2021
In this paper we study algebras with trace and their trace polynomial identities over a field of characteristic 0. We consider two commutative matrix algebras: $D_2$, the algebra of $2\times 2$ diagonal matrices and $C_2$, the algebra of $2 \times 2$ matrices generated by $e_{11}+e_{22}$ and $e_{12}$. We describe all possible traces on these algebras and we study the corresponding trace codimensions. Moreover we characterize the varieties with trace of polynomial growth generated by a finite dimensional algebra. As a consequence, we see that the growth of a variety with trace is either polynomial or exponential.
Polynomial identities for the Jordan algebra of upper triangular matrices of order 2
2012
Abstract The associative algebras U T n ( K ) of the upper triangular matrices of order n play an important role in PI theory. Recently it was suggested that the Jordan algebra U J 2 ( K ) obtained by U T 2 ( K ) has an extremal behaviour with respect to its codimension growth. In this paper we study the polynomial identities of U J 2 ( K ) . We describe a basis of the identities of U J 2 ( K ) when the field K is infinite and of characteristic different from 2 and from 3. Moreover we give a description of all possible gradings on U J 2 ( K ) by the cyclic group Z 2 of order 2, and in each of the three gradings we find bases of the corresponding graded identities. Note that in the graded ca…
Trace Identities on Diagonal Matrix Algebras
2020
Let Dn be the algebra of n × n diagonal matrices. On such an algebra it is possible to define very many trace functions. The purpose of this paper is to present several results concerning trace identities satisfied by this kind of algebras.
Identidades y representaciones del Trabajo Social.
2005
En nuestro trabajo, presentamos el conocimiento de la realidad social desde las dimensiones constructivista e interaccionista, teniendo en cuenta el punto de vista del "público", desde la posición de reconocer una mayor riqueza en el conocimiento que se obtiene desde la "intersubjetividad". En el proceso de investigación, llegamos a la complementariedad metodológica, valiéndonos del enfoque cuantitativo para construir las "imágenes", objetivas y mediante el enfoque cualitativo, contando con la perspectiva del estudio de un caso, las audiencias de una serie "Raquel busca su sitio" obtenemos las imágenes del público o intersubjetivas. Ambos componentes, las imágenes y el público del Trabajo S…
Contatti di popoli ed etnogenesi delle tribù nomadi sahariane
2006
The contribution focuses on the problem of mobility in the Roman world as a means of contact and collaboration. North Africa was in ancient times a land of cultural exchange, of passage of peoples and people. The research dwells on local identities, studies the origins of these peoples, discusses and tries to understand the ancient dynamics, which led them to clash and meet.
Leggere e trasparenti identità
2009
Se la leggerezza e la trasparenza sono divenute caratteristiche ricorrenti nell'ambito dell'architettura, ma anche del design, della moda, dell'arte, è possibile riscontrare un'analoga presenza nel mare magnum delle comunicazioni visive? Si può anche in tale area disciplinare trovare un corrispettivo alleggerimento, non solo della già impalpabile materia adoperata per la composizione degli artefatti, composta da immagini, testi e colori, ma persino delle modalità progettuali che sempre più guardano nei sistemi di identità visiva, a concetti come leggerezza e molteplicità piuttosto che ai loro opposti, rappresentati da pesantezza e unicità? All'interno di questi interrogativi vi è ampio spaz…
Re e lupi mannari: il Lai di Bisclavret e altri esempi dalla letteratura d’oïl
2021
Focusing on identities and conflicts in literature, this article proposes an analysis of the bifid, metamorphic and conflictual figure of the werewolf. Particularly, Marie de France’s Lay of Bisclavret is analyzed in the light of Giorgio Agamben’s philosophical-anthropological theory about the Homo sacer. Comparing the wolf-man to the “sacred man,” this theory not only does it allow us to understand the liminal juridical essence of the werewolf in medieval society, but it also explains the central role of sovereignty in the “recognition” of the wolf-man, in its reintroduction into the civil context of the court, and therefore in the resolution of “conflicts” and in the re-establishment of a…
Black European Inscriptions and the Challenge to Modern Essentialist Identities: The Case of Bernardine Evaristo’s Soul Tourists
2013
This essay shows how the London-born Anglo-Nigerian author Bernardine Evaristo contributes, with her Soul Tourists (2005), to deconstructing modern European nationalist and racially exclusivist models by means of anti-essentialist representational strategies. Centred around the voyage by car and across Europe which, in the late eighties, leads two black Britons, Stanley Williams and Jessie O’Donnell, from England to the Middle East, the novel becomes an imaginative vehicle through which Evaristo represents the black presence as intrinsic to Europe since the th century and foregrounds the substantial contribution of black and mixed-race men and women to the cultural development of Western …