Morita Invariance for Infinitesimal Deformations

Algebras and Representation Theory - Let A and B be two Morita equivalent finite dimensional associative algebras over a field ��. It is well known that Hochschild cohomology is...     

Resveratrol augments ER stress and the cytotoxic effects of glycolytic inhibition in neuroblastoma by downregulating Akt in a mechanism independent of SIRT1

Cancer cells typically display increased rates of aerobic glycolysis that are correlated with tumor aggressiveness and a poor prognosis. Targeting the glycolytic pathway has emerged as an attractive therapeutic route mainly because it should spare normal cells. Here, we evaluate the effects of combining the inhibition of glycolysis with application of the polyphenolic compound resveratrol (RSV) in neuroblastoma (NB) cancer cell lines. Inhibiting glycolysis with 2-deoxy-D-glucose (2-DG) significantly reduced NB cell viability and was associated with increased endoplasmic reticulum (ER) stress and Akt activity. Administration of 2-DG increased the expression of the ER molecular chaperones GRP78 and GRP94, the prodeath protein C/EBP homology protein (CHOP) and the phosphorylation of Akt at S473, T450 and T308. Combined treatment with both RSV and 2-DG reduced GRP78, GRP94 and Akt phosphorylation but increased CHOP and NB cell death when compared with the administration of 2-DG alone. The selective inhibition of Akt activity also decreased 2-DG-induced GRP78 and GRP94 expression and increased CHOP expression, suggesting that Akt can modulate ER stress. Protein phosphatase 1α (PP1α) was activated by RSV, as indicated by a reduction in PP1α phosphorylation at T320. Pretreatment of cells with tautomycin, a selective PP1α inhibitor, prevented the RSV-mediated decrease in Akt phosphorylation, suggesting that RSV enhances 2-DG-induced cell death by activating PP1 and downregulating Akt. The RSV-mediated inhibition of Akt in the presence of 2-DG was not prevented by the selective inhibition of SIRT1, a known target of RSV, indicating that the effects of RSV on this pathway are independent of SIRT1. We propose that RSV inhibits Akt activity by increasing PP1α activity, thereby potentiating 2-DG-induced ER stress and NB cell death.     

On the SO(n + 3) to SO(n) branching multiplicity space

We study the decomposition as an $\text{SO}(3)$-module of the multiplicity space corresponding to the branching from $\text{SO}(n+3)$ to $\text{SO}(n)$. Here, $\text{SO}(n)$ (resp. $\text{SO}(3)$) is considered embedded in $\text{SO}(n+3)$ in the upper left-hand block (resp. lower right-hand block). We show that when the highest weight of the irreducible representation of $\text{SO}(n)$ interlaces the highest weight of the irreducible representation of $\text{SO}(n+3)$, then the multiplicity space decomposes as a tensor product of $?(n+2)/2?$ reducible representations of $\text{SO}(3)$.