1,720,988 research outputs found
Central polynomials of graded algebras: Capturing their exponential growth
Full text linkLet G be a finite abelian group and let A be an associative G-graded algebra over a field of characteristic zero. A central G-polynomial is a polynomial of the free associative G-graded algebra that takes central values for all graded substitutions of homogeneous elements of A. We prove the existence and the integrability of two limits called the central G-exponent and the proper central G-exponent that give a quantitative measure of the growth of the central G-polynomials and the proper central G-polynomials, respectively. Moreover, we compare them with the G-exponent of the algebra
Codimension growth of algebras with superautomorphism
Full text linkLet A be a finite dimensional algebra endowed with a superautomorphism over a field of characteristic zero. In this paper we study the asymptotic behavior of the sequence of phi-codimensions c phi / n(A), n = 1, 2, .... More precisely, we shall prove that limn ->infinity n c phi n(A) always exists and it is an integer related in an explicit way to the dimension of a suitable semisimple subalgebra of A. This result gives a positive answer to a conjecture of Amitsur in this setting. In the final part of the paper we characterize the algebras whose exponential growth is bounded by 2. (c) 2025 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
I risultati di un modello sperimentale di orientamento: il progetto Mobilità Sociale e Merito
No full textMinimal star-varieties of polynomial growth and bounded colength
Full text linkLet V be a variety of associative algebras with involution * over a field F of characteristic zero. Giambruno and Mishchenko proved in that the *-codimension sequence of V is polynomially bounded if and only if V does not contain the commutative algebra D=FâF, endowed with the exchange involution, and M, a suitable 4-dimensional subalgebra of the algebra of 4Ã4 upper triangular matrices, endowed with the reflection involution. As a consequence the algebras D and M generate the only varieties of almost polynomial growth. In the authors completely classify all subvarieties and all minimal subvarieties of the varieties var*(D) and var*(M). In this paper we exhibit the decompositions of the *-cocharacters of all minimal subvarieties of var*(D) and var*(M) and compute their *-colengths. Finally we relate the polynomial growth of a variety to the *-colengths and classify the varieties such that their sequence of *-colengths is bounded by three
Varieties of superalgebras of polynomial growth
Full text link2010 Mathematics Subject Classification: 16R10, 16W55, 16P90.Let V^gr be a variety of associative superalgebras over a field F of characteristic zero. It is well-known that V gr can have polynomial or exponential growth. Here we present some classification results on varieties of polynomial growth. In particular we classify the varieties of at most linear growth and all subvarieties of the varieties of almost polynomial growth.∗ The author was partially supported by MIUR of Italy
Rashkova, T. The Robson cubics for matrix algebras with involution (Acta Univ. Apulensis Math. Inform.).
No full textLet R be the free associative algebra over a field K on
generators and let be the free
associative -algebra in one further indeterminate Consider
the set of polynomials in which are satisfied by
the matrix Such polynomials are
called laws over of the matrix Robson in [Robson, J.
C. Polynomials satisfied by matrices. J. Algebra 55 (1978), no.
2, 509--520; MR523471 (80j:15012)] proved that such laws are a
``consequence" of a finite set of laws and for he exhibited
generators called Robson cubics.
Here the author considers the special case when is a
symmetric or skew-symmetric matrix under the transpose
or symplectic involution and gives an explicit form of the Robson
cubics. Some other results are also given in case $n=3.
Some results on ∗-minimal algebras with involution
No full textLet be an associative algebra with involution over a field
of characteristic zero, the ideal of -polynomial
identities of and , the
corresponding sequence of -codimensions. Recall that
is the dimension of the space of multilinear polynomials in
variables in the corresponding relatively free algebra with
involution of countable rank.
\par
When is a finite dimensional algebra, Giambruno and Zaicev [J.
Algebra 222 (1999), no. 2, 471–484; MR1734235 (2000i:16046)] proved
that the limit exists and is an integer
called the -exponent of
\par
Among finite dimensional algebras with the same -exponent a
prominent role is played by the so called -minimal algebras. This
notion was introduced by Di Vincenzo and La Scala in [J. Algebra 317
(2007), no. 2, 642–657; MR2362935 (2008j:16095)]. Recall that a
finite dimensional algebra is -minimal if for any
finite dimensional algebra with involution such that
we have that
\par
In this paper the authors review recent results of the first author
et al regarding -minimal algebras and prove further properties
towards a complete classification of -minimal algebras
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Some varieties of algebras of polynomial growth
No full textWe determine a complete list of finite dimensional algebras generating the subvarieties of var(G) and var(UT_2)
- …
