Search results for " Involution"
showing 10 items of 34 documents
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.
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…
Thymus pathology observed in the MGTX trial
2012
The MGTX trial is the first prospective, randomized clinical trial that aims to evaluate the impact of extended transsternal thymectomy on myasthenic symptoms, prednisone requirements, and quality of life in patients with nonthymomatous, anti-acetylcholine receptor autoantibody-positive myasthenia gravis (MG). Here, we give an overview of the rationale of thymectomy and the standardized macroscopic and histopathological work-up of thymectomy specimens as fixed in MGTX standard operating procedures, including the grading of thymic lymphofollicular hyperplasia and the morphometric strategy to assess thymic involution.
Calpains mediate epithelial-cell death during mammary gland involution: mitochondria and lysosomal destabilization.
2012
Our aim was to elucidate the physiological role of calpains (CAPN) in mammary gland involution. Both CAPN-1 and -2 were induced after weaning and its activity increased in isolated mitochondria and lysosomes. CAPN activation within the mitochondria could trigger the release of cytochrome c and other pro-apoptotic factors, whereas in lysosomes it might be essential for tissue remodeling by releasing cathepsins into the cytosol. Immunohistochemical analysis localized CAPNs mainly at the luminal side of alveoli. During weaning, CAPNs translocate to the lysosomes processing membrane proteins. To identify these substrates, lysosomal fractions were treated with recombinant CAPN and cleaved produc…
Bing meets Sobolev
2019
We show that, for each $1\le p < 2$, there exists a wild involution $\mathbb S^3\to \mathbb S^3$ in the Sobolev class $W^{1,p}(\mathbb S^3,\mathbb S^3)$.
Asymptotics for Capelli polynomials with involution
2021
Let F be the free associative algebra with involution ∗ over a field F of characteristic zero. We study the asymptotic behavior of the sequence of ∗- codimensions of the T-∗-ideal Γ∗ M+1,L+1 of F generated by the ∗-Capelli polynomials Cap∗ M+1[Y, X] and Cap∗ L+1[Z, X] alternanting on M + 1 symmetric variables and L + 1 skew variables, respectively. It is well known that, if F is an algebraic closed field of characteristic zero, every finite dimensional ∗-simple algebra is isomorphic to one of the following algebras: · (Mk(F ), t) the algebra of k × k matrices with the transpose involution; · (M2m(F ), s) the algebra of 2m × 2m matrices with the symplectic involution; · (Mh(F ) ⊕ Mh(F )op, e…
ON THE ASYMPTOTICS OF CAPELLI POLYNOMIALS
2021
Abstract. 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-g…
*-Graded Capelli polynomials and their asymptotics
2022
Let [Formula: see text] be the free *-superalgebra over a field [Formula: see text] of characteristic zero and let [Formula: see text] be the [Formula: see text]-ideal generated by the set of the *-graded Capelli polynomials [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] alternating on [Formula: see text] symmetric variables of homogeneous degree zero, on [Formula: see text] skew variables of homogeneous degree zero, on [Formula: see text] symmetric variables of homogeneous degree one and on [Formula: see text] skew variables of homogeneous degree one, respectively. We study the asymptotic behavior of the sequence of *-graded codimensions of [Formula: se…