Deformations over non-commutative base by Kawamata, Yujiro

“…We make some remarks on deformation theory over non-commutative base. We describe the base algebra of semi-universal non-commutative deformations using vector spaces $T^1$ and $T^2$.…”
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Sur certains invariants des algèbres artiniennes commutatives by Aleksandrov, Alexandre

“…We study properties of algebraic, topological and analytic invariants of commutative artinian algebras and relationships between them. …”
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Thermal correlators and currents of the W 3 $$ {\mathcal{W}}_3 $$ algebra by Sujay K. Ashok, Sanhita Parihar, Tanmoy Sengupta, Adarsh Sudhakar, Roberto Tateo

“…Abstract Two dimensional conformal field theories with the extended W 3 $$ {\mathcal{W}}_3 $$ symmetry algebra have an infinite number of mutually commuting conserved charges, which are referred to as the quantum Boussinesq charges. …”
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Adventures in physics by Poénaru, Valentin

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Sphere quantization of Higgs and Coulomb branches and Analytic Symplectic Duality by Davide Gaiotto

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On the symbol of singular operators in the case of contour with corner points by Vasile Neagu, Petru Moloșnic

“…Gelfand concerning maximal ideals of commutative Banach algebras \cite{GRS}. In the absence of corner points on the integration contour, the results of this work are consistent with the results from [1]. …”
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Spectral multiplier theorems for abstract harmonic oscillators on UMD lattices by van Neerven, Jan, Portal, Pierre, Sharma, Himani

“…We consider operators acting on a UMD Banach lattice $X$ that have the same algebraic structure as the position and momentum operators associated with the harmonic oscillator $-\frac{1}{2}\Delta + \frac{1}{2}|x|^{2} $ acting on $L^{2}(\mathbb{R}^{d})$. …”
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On $p$-convexification of the Banach-Kantorovich lattice by Gavhar B. Zakirova

“…Let $B$ be a complete Boolean algebra, $Q(B)$ the Stone compact of $B$, and let $C_\infty (Q(B))$ be the commutative unital algebra of all continuous functions $x: Q(B) \to [-\infty, +\infty]$, assuming possibly the values $\pm\infty$ on nowhere-dense subsets of $Q(B)$. …”
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The Rank-One property for free Frobenius extensions by Bellamy, Gwyn, Thiel, Ulrich

“…Examples where the result is applicable include graded Hecke algebras, extended affine Hecke algebras, quantized enveloping algebras at roots of unity, non-commutative crepant resolutions of Gorenstein domains and 3 and 4 dimensional PI Sklyanin algebras.In particular, since the multiplicity matrix for restricted rational Cherednik algebras has the rank-one property if and only if its Cartan matrix does, our result provides a different proof of the original conjecture.…”
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When are the classes of Gorenstein modules (co)tilting? by Wang, Junpeng, Liu, Zhongkui, Zhao, Renyu

“…The second is to characterize Gorenstein modules via finitely generated modules, which provides a proof of that left Noetherian rings with finite left Gorenstein global dimension satisfy First Finitistic Dimension Conjecture and a result related to a question posed by Bazzoni in [J. Algebra 320 (2008) 4281-4299]. The last is to give some new characterizations of Dedekind and Prüfer domains and commutative Gorenstein Artin algebras as well as general (possibly not commutative) Gorenstein rings and Ding–Chen rings.…”
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Homological dimension based on a class of Gorenstein flat modules by Dalezios, Georgios, Emmanouil, Ioannis

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On the space of 2d integrable models by Lukas W. Lindwasser

“…Abstract We study infinite dimensional Lie algebras, whose infinite dimensional mutually commuting subalgebras correspond with the symmetry algebra of 2d integrable models. …”
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Plethysm Products, Element– and Plus Constructions by Kaufmann, Ralph M., Monaco, Michael

“…This allows us to prove a commutativity between element and plus constructions, a special case of which was announced earlier. …”
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