Search results for "involution"
showing 10 items of 73 documents
Codimensions of star-algebras and low exponential growth
2020
In this paper we prove that if A is any algebra with involution * satisfying a non-trivial polynomial identity, then its sequence of *-codimensions is eventually non-decreasing. Furthermore, by making use of the *-exponent we reconstruct the only two *-algebras, up to T*-equivalence, generating varieties of almost polynomial growth. As a third result we characterize the varieties of algebras with involution whose exponential growth is bounded by 2.
Classifying Algebras with Graded Involutions or Superinvolutions with Multiplicities of their Cocharacter Bounded by One
2020
Let A be superalgebra over a field of characteristic zero and let ∗ be either a graded involution or a superinvolution defined on A. In this paper we characterize the ∗-algebras whose ∗-cocharacter has multiplicities bounded by one, showing a set of ∗-polynomial identities satisfied by such algebras.
Group identities on symmetric units
2009
Abstract Let F be an infinite field of characteristic different from 2, G a group and ∗ an involution of G extended by linearity to an involution of the group algebra FG. Here we completely characterize the torsion groups G for which the ∗-symmetric units of FG satisfy a group identity. When ∗ is the classical involution induced from g → g − 1 , g ∈ G , this result was obtained in [A. Giambruno, S.K. Sehgal, A. Valenti, Symmetric units and group identities, Manuscripta Math. 96 (1998) 443–461].
Star-fundamental algebras: polynomial identities and asymptotics
2020
We introduce the notion of star-fundamental algebra over a field of characteristic zero. We prove that in the framework of the theory of polynomial identities, these algebras are the building blocks of a finite dimensional algebra with involution ∗ * . To any star-algebra A A is attached a numerical sequence c n ∗ ( A ) c_n^*(A) , n ≥ 1 n\ge 1 , called the sequence of ∗ * -codimensions of A A . Its asymptotic is an invariant giving a measure of the ∗ * -polynomial identities satisfied by A A . It is well known that for a PI-algebra such a sequence is exponentially bounded and exp ∗ ( A ) = lim n → ∞ c n ∗ ( A ) n \exp ^*(A)=\lim _{n\to \infty }\sqrt [n]{c_n^*(A)} can be explicitly compute…
Some characterizations of algebras with involution with polynomial growth of their codimensions
2018
Let A be an associative algebra endowed with an involution ∗ of the first kind and let c ∗n (A) denote the sequence of ∗-codimensions of A. In this paper, we are interested in algebras with involution such that the ∗-codimension sequence is polynomially bounded. We shall prove that A is of this kind if and only if it satisfies the same identities of a finite direct sum of finite dimensional algebras with involution A i , each of which with Jacobson radical of codimension less than or equal to one in A i . We shall also relate the condition of having polynomial codimension growth with the sequence of cocharacters and with the sequence of colengths. Along the way, we shall show that the multi…
Perdersi. Note sul Labirinto
2022
The paper is inspired by a conversation of its author with Sandro Man- cini. Through a series of self-biographical notes, it tries to examine the topological gure of the labyrinth in some of its main mythical- symbolic, mathematical and conceptual articulations. Starting from a famous essay by Italo Calvino, i.e. La s da al labirinto, it seeks in par- ticular to discuss the works of Pierre Rosenstiehl, mathematician and philosopher to whom we owe some of the most re ned analyses on the subject of labyrinth. In the conclusions, after some other short intro- spective remarks, one aims at raising the necessity of more systematic and deepened investigations about this subject.
The J-invariant, Tits algebras and Triality
2012
In the present paper we set up a connection between the indices of the Tits algebras of a simple linear algebraic group $G$ and the degree one parameters of its motivic $J$-invariant. Our main technical tool are the second Chern class map and Grothendieck's $\gamma$-filtration. As an application we recover some known results on the $J$-invariant of quadratic forms of small dimension; we describe all possible values of the $J$-invariant of an algebra with orthogonal involution up to degree 8 and give explicit examples; we establish several relations between the $J$-invariant of an algebra $A$ with orthogonal involution and the $J$-invariant of the corresponding quadratic form over the functi…
Hybridization as Speciation? The Viewpoint of Greek Folk Biology (and Aristotle) on the Mutation of Species
2008
Modern evolutionary biologists, as for example Michael Arnold, attest that hybridizations could have a strong creative force in organismal evolution. Such an idea was considered as blasphemous by 19th century critics on evolutionism, and did not entirely convince Charles Darwin himself, but it would not have surprised the ancient Greeks and Romans, who knew that inter-specific couplings gave birth to new species. These new species, however, were considered as products of a process of "adulteration" or "involution", rather than "evolution".
Differential functions of calpain 1 during epithelial cell death and adipocyte differentiation in mammary gland involution
2014
Calpains become activated in the mammary gland early during weaning, cleaving several proteins located mainly in the cell membrane, but also in other organelles such as lysosomes, mitochondria and nuclei. By immunofluorescence and Western blot analysis, we have demonstrated the nuclear translocation of calpain-1 and calpain-2, together with the cleavage of several cytoplasmic nucleoporins in epithelial cells of the lobulo-alveolar compartment. In vivo and in vitro calpain inhibition prevented this nucleoporin degradation. In addition, calpain-1 was also present in the nucleus of non-epithelial mammary tissue cells, concomitant with adipocyte re-differentiation. Calpain-1 was internalized wi…
Infantile hemangiomas with minimal or arrested growth: A retrospective case series
2018
Background/objectives Infantile hemangiomas (IH) with minimal or arrested growth (MAG) constitute a distinctive subset of IH based on their clinical characteristics and natural history. They are often confused with capillary malformations. Methods A retrospective observational study has been carried out in which clinical and perinatal characteristics have been evaluated in all IH-MAG evaluated in our Dermatology Department in a 5-year period (January 2013-December 2017). Results A total of 14 IH-MAG affecting 13 patients were identified (10 girls and 3 boys). All were born full term, with a mean birth weight of 3448 g for girls vs 3540 g for boys, corresponding to the 72nd percentile for bo…