4,173 research outputs found
On Multiple Polynomials of Capelli Type
No full textThis paper deals with the class of Capelli polynomials in free associative algebra F{Z} (where F is an arbitrary field, Z is a countable set) generalizing the construction of multiple Capelli polynomials. The fundamental properties of the introduced Capelli polynomials are provided. In particular, decomposition of the Capelli polynomials by means of the same type of polynomials is shown. Furthermore, some relations between their T -ideals are revealed. A connection between double Capelli polynomials and Capelli quasi-polynomials is established
Quasi-polynomials of Capelli. III
No full textIn this paper polynomials of Capelli type (double and quasi-polynomials of Capelli) belonging to a free associative algebra considering over an arbitrary field and generated by two disjoint countable sets are investigated. It is shown that double Capelli's polynomials , are consequences of the standard polynomial . Moreover, it is proved that these polynomials equal to zero both for square and for rectangular matrices of corresponding sizes. In this paper it is also shown that all Capelli's quasi-polynomials of the degree are minimal identities of odd component of -graded matrix algebra for any and
Norberto Capelli, piano (Argentina) y Héctor Moreno, piano (Argentina)
No full textConcierto interpretado por Norberto Capelli y Héctor Moreno, pianistas argentinos residentes en Florencia. Se formaron musicalmente en su país natal con reconocidos maestros. Desarrollaron individualmente sus carreras como solistas y pianistas de música de cámara y fue en 1974 en que decidieron formar este dúo, interesados por las amplias posibilidades que ofrecen al pianista los repertorios de dos pianos y piano a cuatro manos.
En este concierto interpretaron obras de W. A. Mozart, F. Schubert, C. Debussy y F. Liszt
Erratum: Envisioning translational hyperscanning: how applied neuroscience might improve family-centered care (Social Cognitive and Affective Neuroscience (2022) (nsac061) DOI: 10.1093/scan/nsac061)
No full textThis is a correction to: Elisa Roberti, Elena Capelli, Livio Provenzi Envisioning translational hyperscanning: how applied neuroscience might improve family-centered care, Social Cognitive and Affective Neuroscience, 2022; nsac061, https://doi.org/10.1093/scan/nsac061 In the originally published version of this manuscript, the order of authors and the authors’ affiliations were incorrectly given as follows: Livio Provenzi,1,2 Elisa Roberti,2 and Elena Capelli2 1Department of Brain and Behavioral Sciences, University of Pavia, Pavia 27100, Italy 2Developmental Psychobiology Lab, IRCCS Mondino Foundation, Pavia 27100, Italy The Publisher apologizes for this error, which occurred during the production process. The author list and authors’ affiliations have now been corrected, as follows: Elisa Roberti,1 Elena Capelli,1 and Livio Provenzi2,1 1Developmental Psychobiology Lab, IRCCS Mondino Foundation, Pavia 27100, Italy 2Department of Brain and Behavioral Sciences, University of Pavia, Pavia 27100, Ital
ON THE ASYMPTOTICS OF CAPELLI POLYNOMIALS
No full textAbstract. We present old and new results about Capelli polynomials, Z2-graded Capelli
polynomials and Capelli polynomials with involution and their asymptotics.
Let Capm = Pσ2Sm (sgnσ)tσ(1)x1tσ(2) · · · tσ(m−1)xm−1tσ(m) be the m-th Capelli
polynomial of rank m. In the ordinary case (see [33]) it was proved the asymptotic
equality between the codimensions of the T -ideal generated by the Capelli polynomial
Capk2+1 and the codimensions of the matrix algebra Mk(F ). In [9] this result was
extended to superalgebras proving that the Z2-graded codimensions of the T2-ideal generated by the Z2-graded Capelli polynomials Cap0 M+1 and Cap1 L+1 for some fixed M,
L, are asymptotically equal to the Z2-graded codimensions of a simple finite dimensional
superalgebra. Recently, the authors proved that the ∗-codimensions of a ∗-simple finite dimensional algebra are asymptotically equal to the ∗-codimensions of the T-∗-ideal
generated by the ∗-Capelli polynomials Cap+ M+1 and Cap− L+1, for some fixed natural
numbers M and L
The evolutionary history of Southern Africa
No full textThe genomic variability of Southern African groups is characterised by an exceptional degree
of diversity, which is the result of long-term local evolutionary history, migrations and
gene-flow. Over the last few years several investigations have characterized the signatures of
these processes, revealing how ancient and more recent events have shaped the structure and
ancestry composition of local populations. Here we discuss recent insights into the genetic
history of the Southernmost part of the African continent provided by the analysis of modern
and ancient genomes. Future work is expected to clarify the population dynamics associated
with the emergence of H. sapiens across Africa and the details of the process of dispersion
and admixture associated with the arrival of Bantu-speaking groups in the region
Nuovi dati archeologici e archeometrici sulle anfore greco-italiche: i relitti di III secolo del Mediterraneo occidentale e la possibilità di una nuova classificazione
No full textAsymptotics for the Amitsur's Capelli - Type Polynomials and Verbally Prime PI-Algebras
No full textWe consider associative PI-algebras over a field of characteristic zero. The
main goal of the paper is to prove that the codimensions of a verbally prime
algebra [11] are asymptotically equal to the codimensions of the T-ideal generated
by some Amitsur’s Capelli-type polynomials E¤M;L [1]. In particular we
prove that
cn(Mk(G)) '' cn(E¤k2;k2 )
and
cn(Mk;l(G)) '' cn(E¤k2+l2;2kl);
where G is the Grassmann algebra. These results extend to all verbally prime
PI-algebras a theorem of A.Giambruno and M.Zaicev [9] giving the asymptotic
equality
cn(Mk(F)) '' cn(E¤k2;0)
between the codimensions of the matrix algebra Mk(F) and the Capelli polynomials
On the asymptotics for -Capelli identities
No full textLet Fbe the free associative algebra with involution ∗ over a field of characteristic zero. If L and M are two natural numbers let Γ∗_M+1,L+1 denote theT∗-idealofFgenerated by the∗-capellipolynomialsCap+M+1,Cap−L+1 alternanting on M+1 symmetric variables and L+1skew variables,respectively.It is well known that, if F is an algebraic closed field, every finite dimensional ∗-simple algebra is isomorphic to one of the following algebras (see [4], [2]):· (Mk(F),t) with the transpose involution; · (M2m(F),s) with the symplectic involution; · (Mk(F)⊕Mk(F)op,∗) with the exchange involution. The aim of this talk is to show a relation among the asymptotics of the∗-codimensions of the finite dimensional ∗-simple algebras and the T∗-ideals Γ∗M+1,L+1, for some fixed natural numbers M and L. In particular: c∗n(Γ∗k(k+1)/2,k(k−1)/2)=c∗n((Mk(F),t)), c∗n(Γ∗m(2m−1),m(2m+1))=c∗n((M2m(F),s)) and c∗n(Γ∗k2,k2)c∗n((Mk(F)⊕Mk(F)op,∗)). Similar results have been found for simple finite dimensional superalgebras in [1] and these extend a theorem of Giambruno and Zaicev [3] giving in the ordinary case the asymptotic equality between the codimensions of the Capelli polynomials and the codimensions of the matrix algebra.This talk is based on a joint work with A. Valenti.
References [1] F. Benanti, Asymptotics for Graded Capelli Polynomials, Algebra Repres. Theory18 (2015), 221–233.[2] A.GiambrunoandM.Zaicev, PolynomialIdentitiesandAsymptoticsMethods, Surveys, vol. 122, American Mathematical Society, Providence, RI, 2005. [3] A. Giambruno and M. Zaicev, Asymptotics for the Standard and the Capelli
Identities, Israel J. Math.135 (2003), 125–145. [4] L.H.Rowen,PolynomialIdentitiesinRingTheory,AcademicPress,NewYork, 198
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