Search results for " involution"

Graded involutions on upper-triangular matrix algebras

2009

Capelli identities on algebras with involution or graded involution

2022

We present recent results about Capelli polynomials with involution or graded involution and their asymptotics. In the associative case, the asymptotic equality between the codimensions of the T -ideal generated by the Capelli polynomial of rank k2 + 1 and the codimensions of the matrix algebra Mk(F) was proved. This result was extended to superalgebras. Recently, similar results have been determined by the authors in the case of algebras with involution and superalgebras with graded involution.

On the asymptotics for $ast$-Capelli identities

Let 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 ∗…

Nitration of cathepsin D enhances its proteolytic activity during mammary gland remodelling after lactation

2009

Proteomic studies in the mammary gland of control lactating and weaned rats have shown that there is an increased pattern of nitrated proteins during weaning when compared with controls. Here we report the novel finding that cathepsin D is nitrated during weaning. The expression and protein levels of this enzyme are increased after 8 h of litter removal and this up-regulation declines 5 days after weaning. However, there is a marked delay in cathepsin D activity since it does not increase until 2 days post-weaning and remains high thereafter. In order to find out whether nitration of cathepsin D regulates its activity, iNOS (inducible nitric oxide synthase)−/− mice were used. The expression…

Some results on ∗-minimal algebras with involution

2009

Let $(A, *)$ be an associative algebra with involution over a field $F$ of characteristic zero, $T_*(A)$ the ideal of $*$-polynomial identities of $A$ and $c_n(A, *),$ $n=1, 2, \ldots$, the corresponding sequence of $*$-codimensions. Recall that $c_n(A, *)$ is the dimension of the space of multilinear polynomials in $n$ variables in the corresponding relatively free algebra with involution of countable rank. \par When $A$ is a finite dimensional algebra, Giambruno and Zaicev [J. Algebra 222 (1999), no. 2, 471–484; MR1734235 (2000i:16046)] proved that the limit $$\exp(A, *)=\lim_{n\to \infty}\sqrt[n]{c_n(A, *)}$$ exists and is an integer called the $*$-exponent of $A.$ \par Among finite dime…

Subcellular distribution of calpain-1 and calpain-2 as a key event for calpain-mediated functions in physiological and neoplastic mammary models

2019

Calpains are a family of calcium-dependent proteases, which modulate their substrates rather than degrade them in such a way that modifies them. Calpains deregulations have been determined as an aggravating factor of different diseases, including cancer. Nevertheless, there are no clear records about the particular contribution of each calpain isoform in physiological processes and how these isoforms are deregulated in pathological conditions. In vivo, each calpain isoform recognizes specific proteins as substrates, and it has been suggested that calpains subcellular localization might determine their substrate recognition, and consequently their functions. In the present study we have expl…

Group gradings on associative algebras with involution

2008

Are zinc-bound metallothionein isoforms (I+II and III) involved in impaired thymulin production and thymic involution during ageing?

2004

Abstract Background With advancing age, thymic efficiency shows progressive decline due to thymic involution allowing impaired cell-mediated immunity and the appearance of age-related diseases. The intrinsic cause of thymic involution is still undefined. Chronic inflammation and high glucocorticoids (GCs) may be involved. However, transgenic mice, with increased GC sensitivity and over expression of GC receptors, display delayed age-associated thymic involution. This fact suggests that other substances may affect thymic involution. Among them, both isoforms of metallothioneins (MTs) I+II and III are the major candidates because their increments leads to organ atrophy in constant stress and …

NF-ĸB as node for signal amplification during weaning.

2011

Post-lactational involution has been reported to share common features with breast tumor development. A deep characterization of the signaling triggered after weaning would help to unveil the complex relationship between involution and breast cancer. NF-κB, a crucial factor in the involuting gland, might be an important regulatory node for signal amplification after weaning; however there is limited information about the identity of NF-κB-target genes and the molecular mechanisms leading to the selection of genes involved in a particular biological process. We identified 4532 target genes in mammary gland at 48h weaning, by genome-wide analysis of regions bound by RelA(p65)-NF-κB in vivo. I…

Nitric oxide triggers mammary gland involution after weaning: remodelling is delayed but not impaired in mice lacking inducible nitric oxide synthase

2010

During mammary gland involution, different signals are required for apoptosis and tissue remodelling. To explore the role of NO in the involution of mammary tissue after lactation, NOS2 (inducible nitric oxide synthase)-KO (knockout) mice were used. No apparent differences were observed between NOS2-KO and WT (wild-type) animals during pregnancy and lactation. However, upon cessation of lactation, a notable delay in involution was observed, compared with WT mice. NOS2-KO mice showed increased phosphorylation of STAT (signal transducer and activator of transcription) 5 during weaning, concomitant with increased beta-casein mRNA levels when compared with weaned WT glands, both hallmarks of th…